This is just a compilation of data I've tracked over time. It's really for sheer personal curiosity, but I've seen people refer to my essence drop data, so I guess it has some use to others too.

Directory.
Frequency of essence drops from nurtures
Levels for bred pets
Frequency of gem and tome drops from grove named
Data on puff and vene shops
Wild nest rarity data

Essence Drops from Nurtures.
...that is, a list of when I got essences to drop from nurtures, and how many total scales I had earned at that point.

180/800,755 = ~0.0225%

21/180 are enhanced: 11.67%

Smallest number between essences: 14
Largest number between essences: 22,119
Average number between essences: 4903

1. 12/27/17: Regular Kelpari Essence (744,439)
2. 12/27/17: Regular Aurleon Essence (747,911)
3. 12/28/17: Regular Ny'vene Essence (750,308)
4. 12/29/17: Enhanced Bulbori Essence (759,627)
5. 12/30/17: Enhanced Sylvorpa Essence (762,325)
6. 1/3/18: Regular Zolnixi Essence (773,003)
7. 1/3/18: Regular Aurleon Essence (773,071)
8. 1/4/18: Regular Luffox Essence (775,416)
9. 1/4/18: Regular Sylvorpa Essence (775,620)
10. 1/5/18: Regular Nephini Essence (780,594)
11. 1/13/18: Regular Griffi Essence (786,939)
12. 5/29/18: Regular Aeridini Essence (802,492)
13. 5/29/18: Regular Zolnixi Essence (803,165)
14. 5/29/18: Regular Zolnixi Essence (810,748)
15. 5/30/18: Regular Faelora Essence (818,700)
16. 5/31/18: Regular Ferrikki Essence (822,539)
17. 5/31/18: Regular Draeyl Essence (823,833)
18. 6/1/18: Enhanced Nytekrie Essence (827,840)
19. 6/2/18: Enhanced Zolnixi Essence (831,121)
20. 6/2/18: Regular Nephini Essence (833,427)
21. 6/8/18: Regular Nephini Essence (838,815)
22. 6/10/18: Regular Nephini Essence (860,646)
23. 7/1/18: Regular Lupora Essence (863,743)
24. 7/15/18: Regular Lupora Essence (865,611)
25. 7/16/18: Regular Lupora Essence (866,137)
26. 8/21/18: Regular Zolnixi Essence (884,450)
27. 8/22/18: Regular Vulnyx Essence (893,569)
28. 8/22/18: Regular Qitari Essence (894,659)
29. 8/23/18: Enhanced Aeridini Essence (896,242)
30. 8/25/18: Regular Faelora Essence (905,074)
31. 8/25/18: Regular Kelpari Essence (909,724)
32. 8/28/18: Regular Sylvorpa Essence (913,613)
33. 8/29/18: Regular Morkko Essence (916,343)
34. 8/31/18: Regular Nytekrie Essence (917,374)
35. 8/31/18: Regular Qitari Essence (919,200)
36. 9/3/18: Regular Zolnixi Essence (928,092)
37. 9/6/18: Regular Ferrikki Essence (929,859)
38. 9/7/18: Regular Morkko Essence(932,220)
39. 9/7/18: Regular Morkko Essence (937,705)
40. 9/8/18: Regular Kelpari Essence (944,098)
41. 9/29/18: Regular Lupora Essence (946,356)
42. 11/8/18: Regular Luffox Essence (967,311)
43. 11/9/18: Regular Zolnixi Essence (972,442)
44. 11/10/18: Regular Sylvorpa Essence (976,337)
45. 11/13/18: Regular Vulnyx Essence (986,684)
46. 12/27/18: Regular Lupora Essence (993,064)
47. 12/27/18: Regular Sylvorpa Essence (994,410)
48. 12/27/18: Regular Nephini Essence (996,984)
49. 12/27/18: Regular Draeyl Essence (997,498)
50. 12/28/18: Enhanced Vulnyx Essence (999,424)
51. 12/28/18: Regular Nephini Essence (1,004,865)
52. 12/28/18: Enhanced Vulnyx Essence (1,005,270)
53. 1/4/19: Regular Ferrikki Essence (1,022,471)
54. 1/5/19: Regular Nephini Essence (1,029,542)
55. 1/12/19: Regular Qitari Essence (1,051,661)
56. 1/12/19: Regular Faelora Essence (1,052,950)
57. 1/15/19: Regular Puffadore Essence (1,064,631)
58. 1/16/19: Regular Morkko Essence (1,071,506)
59. 2/1/19: Regular Draeyl Essence (1,075,694)
60. 3/18/19: Regular Qitari Essence (1,083,540)
61. 3/22/19: Regular Qitari Essence (1,083,881)
62. 4/25/19: Regular Vulnyx Essence (1,087,146)
63. 4/28/19: Enhanced Lupora Essence (1,088,660)
64. 4/4/19: Regular Lighira Essence (1,095,969)
65. 5/7/19: Regular Vulnyx Essence (1,114,126)
66. 5/13/19: Regular Kelpari Essence (1,116,770)
67. 5/20/19: Regular Lupora Essence (1,119,657)
68. 5/22/19: Regular Aeridini Essence (1,120,030)
69. 7/3/19: Regular Lighira Essence (1,126,657)
70. 7/4/19: Regular Ferrikki Essence (1,128,105)
71. 7/5/19: Regular Lupora Essence (1,129,467)
72. 7/25/19: Enhanced Lupora Essence (1,130,607)
73. 8/12/19: Regular Luffox Essence (1,139,401)
74. 8/13/19: Enhanced Lupora Essence (1,146,339)
75. 8/13/19: Regular Zolnixi Essence (1,147,428)
76. 8/13/19: Regular Ferrikki Essence (1,147,504)
77. 8/13/19: Enhanced Ryori Essence (1,150,816)
78. 8/13/19: Regular Kelpari Essence (1,152,452)
79. 8/13/19: Regular Sylvorpa Essence (1,157,595)
80. 8/13/19: Regular Sylvorpa Essence (1,157,609)
81. 8/14/19: Regular Puffadore Essence (1,161,902)
82. 8/14/19: Regular Aeridini Essence (1,163,378)
83. 8/14/19: Regular Puffadore Essence (1,163,642)
84. 8/15/19: Regular Griffi Essence (1,168,877)
85. 8/15/19: Regular Lunemara Essence (1,171,948)
86. 8/15/19: Regular Zolnixi Essence (1,178,104)
87. 8/16/19: Regular Lunemara Essence (1,183,921)
88. 8/16/19: Regular Sylvorpa Essence (1,184,166)
89. 8/16/19: Regular Ferrikki Essence (1,192,364)
90. 8/16/19: Regular Qitari Essence (1,197,440)
91. 8/21/19: Enhanced Qitari Essence (1,209,476)
92. 8/22/19: Regular Puffadore Essence (1,215,832)
93. 8/22/19: Regular Kelpari Essence (1,223,549)
94. 8/23/19: Enhanced Sylvorpa Essence (1,229,863)
95. 8/23/19: Regular Sylvorpa Essence (1,230,621)
96. 8/23/19: Regular Puffadore Essence (1,236,434)
97. 8/31/19: Regular Ferrikki Essence (1,247,735)
98. 8/31/19: Regular Griffi Essence (1,251,277)
99. 9/2/19: Regular Kelpari Essence (1,255,532)
100. 9/2/19: Regular Vulnyx Essence (1,256,250)
101. 10/1/19: Enhanced Nephini Essence (1,260,580)
102. 11/1/19: Regular Faelora Essence (1,265,223)
103. 11/2/19: Regular Draeyl Essence (1,268,528)
104. 11/2/19: Regular Zolnixi Essence (1,270,769)
105. 11/2/19: Regular Aurleon Essence (1,271,327)
106. 11/2/19: Regular Nephini Essence (1,271,484)
107. 11/3/19: Regular Lupora Essence (1,279,218)
108. 11/15/19: Regular Bulbori Essence (1,292,576)
109. 11/22/19: Regular Lighira Essence (1,296,941)
110. 1/3/19: Regular Bulbori Essence (1,318,323)
111. 1/4/19: Regular Aurleon Essence (1,319,934)
112. 1/4/19: Regular Lighira Essence (1,320,915)
113. 1/4/19: Regular Luffox Essence (1,321,580)
114. 1/6/19: Regular Nytekrie Essence (1,326,015)
115. 1/6/19: Regular Griffi Essence (1,326,063)
116. 1/6/19: Regular Zolnixi Essence (1,330,850)
117. 1/7/19: Regular Qitari Essence (1,332,324)
118. 1/7/19: Regular Morkko Essence (1,332,675)
119. 1/7/19: Regular Lunemara Essence (1,334,247)
120. 1/7/19: Regular Zolnixi Essence (1,336,585)
121. 1/7/19: Regular Bulbori Essence (1,337,015)
122. 1/7/19: Regular Zolnixi Essence (1,337,669)
[Nurture Grounds Update occurred here]
123. 2/14/20: Regular Lunemara Essence (1,351,979)
124. 2/15/20: Regular Lunemara Essence (1,353,837)
125. 2/17/20: Regular Lupora Essence (1,356,702)
126. 2/18/20: Regular Nephini Essence (1,357,727) - BOOSTED
127. 2/18/20: Regular Griffi Essence (1,357,895) - BOOSTED
128. 2/22/20: Regular Qitari Essence (1,360,105)
129. 3/21/20: Regular Ryori Essence (1,372,365) - BOOSTED
130. 4/8/20: Enhanced Lupora Essence (1,376,675)
131. 5/13/20: Regular Morkko Essence (1,383,377)
132. 5/27/20: Regular Luffox Essence (1,395,670)
133. 5/27/20: Regular Griffi Essence (1,404,933)
134. 5/28/20: Regular Aurleon Essence (1,410,416)
135. 5/28/20: Regular Griffi Essence (1,413,448)
136. 5/28/20: Enhanced Qitari Essence (1,419,959)
137. 5/28/20: Regular Zolnixi Essence (1,420,954)
138. 5/29/20: Regular Qitari Essence (1,425,582)
139. 5/29/20: Regular Kelpari Essence (1,430,232)
140. 5/29/20: Regular Aurleon Essence (1,434,504)
141. 5/29/20: Regular Griffi Essence (1,436,275)
142. 5/30/20: Regular Ferrikki Essence (1,437,658) - BOOSTED
143. 5/30/20: Enhanced Zolnixi Essence (1,442,278)
144. 5/30/20: Regular Faelora Essence (1,446,674)
145. 5/30/20: Enhanced Faelora Essence (1,447,998)
146. 5/30/20: Regular Zolnixi Essence (1,450,534)
147. 5/31/20: Regular Lupora Essence (1,452,267)
148. 5/31/20: Regular Lunemara Essence (1,454,108)
149. 5/31/20: Regular Qitari Essence (1,457,940)
150. /5/31/20: Regular Lupora Essence (1,462,185)
151. 5/31/20: Regular Kelpari Essence (1,462,678)
152. 5/31/20: Regular Bulbori Essence (1,462,792)
153. 5/31/20: Regular Sylvorpa Essence (1,463,975)
154. 5/31/20: Regular Kelpari Essence (1,464,112)
155. 5/31/20: Regular Vulnyx Essence (1,464,195)
156. 6/5/20: Regular Lunemara Essence (1,469,426)
157. 6/5/20: Regular Vulnyx Essence (1,474,727)
158. 6/5/20: Regular Ryori Essence (1,476,014)
159. 6/5/20: Regular Kelpari Essence (1,476,636)
160. 6/5/20: Regular Luffox Essence (1,478,969)
161. 6/9/20: Regular Kelpari Essence (1,483,546)
162. 6/9/20: Regular Zolnixi Essence (1,484,117)
163. 6/9/20: Regular Zolnixi Essence (1,484,806)
164. 6/9/20: Regular Sylvorpa Essence (1,485,334)
165. 6/24/0: Regular Lupora Essence (1,489,930)
166. 7/3/20: Regular Aeridini Essence (1,492,490)
167. 8/7/20: Regular Zolnixi Essence (1,501,561)
168. 8/9/20: Regular Nytekrie Essence (1,504,393)
169. 8/21/20: Regular Ryori Essence (1,512,123)
170. 8/21/20: Regular Bulbori Essence (1,515,455)
171. 8/22/20: Regular Luffox Essence (1,518,610)
172. 8/23/20: Enhanced Kelpari Essence (1,520,171)
173. 8/27/20: Regular Qitari Essence (1,522,545)
174. 8/28/20: Regular Bulbori Essence (1,531,358)
175. 8/28/20: Regular Morkko Essence (1,532,397)
176. 8/29/20: Regular Ferrikki Essence (1,535,366)
177. 8/29/20: Regular Sylvorpa Essence (1,535,621)
178. 8/29/20: Regular Vulnyx Essence (1,536,951)
179. 8/30/20: Enhanced Lunemara Essence (1,544,197)
180. 8/30/20: Enhanced Ryori Essence (1,545,194)
181. 9/1/20: Regular Ferrikki Essence (1,552,445)
182. 9/7/20: Regular Zolnixi Essence (1,555,702)
183. 9/8/20: Enhanced Griffi Essence (1,560,646)
184. 9/9/20: Regular Luffox Essence (1,563,298)
185. 9/12/20: Regular Zolnixi Essence (1,564,585)
186. 12/27/20: Regular Vulnyx Essence (1,586,237)
187. 1/5/21: Enhanced Faelora Essence (1,602,501)
188. 1/5/21: Regular Bulbori Essence (1,602,947)
189. 3/18/21: Enhanced Zolnixi Essence (1,606,850)
190. 5/17/21: Regular Zolnixi Essence (1,616,175)
191. 5/17/21: Regular Faelora Essence (1,617,885)
192. 5/17/21: Regular Kelpari Essence (1,619,673)
193. 5/18/21: Regular Sylvorpa Essence (1,625,582)
194. 5/19/21: Regular Zolnixi Essence (1,633,365)
195. 5/19/21: Regular Zolnixi Essence (1,633,968)
196. 5/20/21: Regular Qitari Essence (1,636,020)

How the heck do egg levels work, since it came up in region chat.
(for this "research" I'm just gonna pull random pets off AS. numbers listed are the parents' levels)

I have literally no idea how to do math on this so if someone else wants to help with that, be my guest

Level 0
-if both parents are lv0, their offspring will be lv0
-if the egg is tamed it will be lv0
-if the egg is exclusive it will be lv0

Level 1
0 and 16
0 and 17
0 and 18
0 and 21
0 and 22
0 and 31
0 and 45
0 and 46
0 and 51
0 and 63
0 and 66
1 and 40
3 and 25
4 and 17
4 and 67
5 and 11
5 and 15
5 and 70
6 and 10
7 and 32
7 and 50
8 and 17
9 and 14
9 and 29
14 and 19
16 and 17
17 and 40
19 and 20

Level 2
0 and 22
0 and 25
0 and 26
0 and 31
0 and 46
0 and 49
0 and 60
0 and 70
2 and 33
5 and 31
6 and 28
15 and 26
16 and 32
22 and 28
26 and 28

Level 3
0 and 43
0 and 60
0 and 61
0 and 70
3 and 64
3 and 65
5 and 60
5 and 67
7 and 70
8 and 60
23 and 34
25 and 70
28 and 40
30 and 30*
30 and 70
33 and 60
37 and 37*

Level 4
0 and 43
0 and 45
0 and 46
0 and 61
0 and 62
0 and 68
0 and 69
0 and 70
7 and 60
7 and 61
7 and 70
9 and 45
41 and 45
49 and 49*

Level 5
0 and 60
0 and 64
0 and 70
2 and 59
3 and 57
5 and 69
23 and 64
30 and 70
36 and 70
44 and 70
48 and 65
50 and 70
59 and 60

Level 6
5 and 63
48 and 69
55 and 70
56 and 65
61 and 69

(sorry, I'm getting lazy and/or need to do homework)

reserved

NOTE: Krin stated that gems and tomes had the same drop rate, so the differences in my data between them are likely due to RNG. HOWEVER, he has now added a script so that once you have enough tomes to unlock all the equips, it will instead drop a gem. As such, I am discontinuing this data - I should only be getting gem drops from now on. But I'll leave it up as a kinda curiosity thing, and since I already put this much work into collecting the data.

Gems can drop from any named in the grove.
Total gem drops: 36/334 = 10.78%
-From Demora: 9/62 = 14.52%
-From Dia: 3/55 = 5.45%
-From Kowlla: 5/54 = 9.26%
-From Eleane: 6/50 = 12%
-From Malfarian: 8/58 = 13.79%
-From Oakstout: 5/55 = 9.09%

Tomes can drop from any of the cave named.
Total tome drops: 31/171 = 18.13%
-From Demora: 10/62 = 16.13%
-From Dia: 9/55 = 16.36%
-From Kowlla (and door): 9/54 = 22.22%

Data:
Note: one asterisk is a gem; two asterisks is a tome.
A slash next to Kowlla data indicates that the tome was acquired from the door. So far I haven't gotten any gems from there.
OKMEDh*
OK
ODeE*
MDhEK\**
MODhDe
MKO
MDeEK*Dh
O
ODh
MDe**
E*KK
ODhK
ODe**E
M*De
DhDe*
M*OK
Dh**
E
De**MDhDeK
OE
DeDe
ODeMEDhK**
DhDe
M*ODh
K
E
MK
Dh
K
De
O*E
Dh
K**
M
OEDe
DhOK
MDeK
EODh
DeMDhK
OE
MK
ODe
MEDh
MKEDhDe
OM
K
O
Dh
MDe**De
EDh
DeODhK
OE
M*De
De
E*MK
ODh*De*K
E
MK
De**ODhK
ME
DeK\**
De
O
OM*E
OK
MODh
MDe*
DhK
EDe
MOK
ODe
EDh*
MM
EK
De
O
M
Dh
EDe
DhK
O
De
M
K\**
EDh**O
OODe
MEK
Dh
EDeODH**
M
K
Dh
O*EDe**&*K
MMDh
E
De
ODh
ME
KDe
ODh
Dh
De**KM
MOE
DeK*
DH**ODe
MK*E
DhDe*&**
ODh**De
O
K*MME
MO*E
MDeDh
KODeEDh
M*
DhK**
DeOE
K**M
Dh**E*DeDe*&**
OK**ME
Dh**
DeDe
EK
DhMO
E
EDeK**ODh
E
M
DeO*DhDe
DhME
K
E
M*ODhDhDe*KM
OEK
MDeDh
O*
Dh*&**M
K*\**\**
E
De
OM*K
Dh**
EDhDe
DeK
O
De
M
(^spreadsheet and math done up to this point^)
EK**
K**Dh
(Krin's changes occurred here - end of data for calculations. Beyond this point is gem-only data for sheer curiosity.)
De1MDh
ODh1
MK
E
E
De
OE
DhKM
DeDe
O
E
Dh1K
M
ED1
MO
K
MEDh
OO
K1DhDe
MDeE
O1KKE1
OMDhDe1
E
De1OK1
KMDh1
EMDe1
OO
K
De
Dh1
ME1
ODh2
K1
O1EDe
De
MDhK
EDh
O
M
DhDe
K
K
EDh
ODhDeM
K
MDeO
E
DhK
De
M
OEKEDh
De1De
MO
M
Dh
EK
O
DeM
K\1
Di1
E
O
M
ODe
De
MDhK
E
Dh
O
M
OE
ODe1
KM1
Dh
O1E
M
K
D
E

reserved

Puff and Vene shop data.
Note that stats (including mana) do increase as price/rarity increases.
*Notes with asterisks are extrapolated guesses and may not be accurate.

Data:
*<200: 1c?
*200s: 2c?
328 vene: 1v
*400s: 4c?
598 vene: 1v2c
682 vene: 2v
703 vene: 1v2c - this is weird
1426 vene: 1v4c
1474 vene: 2v2c
1571 vene: 3v
a 2789 vene had 3 vis genes, was probably mythical, couldn't afford though :(

78 puff: 2c
149 puff: 1v (at least - untested)
779 puff: 2v4c
1300 puff: 4v

Things you can do during battle:
-Breed
-Hatch eggs
-Generate pets
-Tend to fest plants, etc.
-Nurture
-Accept trades

Things you can't do during battle:
-Finish or accept missions
-Buy pets
-Anything in your inventory (using items, putting things on broker, etc.)
-Switch your party
-Use potions
-Feed pets

Wild Nests
Sweet Blossom Orchard and Astryl's Tranquility
Val found a myth egg from AT
Uncommon: 42/54
Rare: 11/54
Epic: 1/54

1. rare (2c)
2. rare (2c)
3. uncommon (1c)
4. rare (1v)
5. uncommon (1c)
6. uncommon (1c)
7. uncommon (1c)
8. uncommon (1c)
9. uncommon (1c)
10. uncommon (1c)
11. uncommon (1c)
12. uncommon (1c)
13. uncommon (1c)
14. uncommon (1c)
15. rare (1v)
16. rare (2c)
17. rare (2c)
18. rare (2c)
19. uncommon (1c)
20. uncommon (1c)
21. uncommon (1c)
22. uncommon (1c)
23. uncommon (1c)
24. uncommon (1c)
25. uncommon (1c)
26. epic (2v)
27. uncommon (1c)
28. uncommon (1c)
29. uncommon (1c)
30. uncommon (1c)
31. uncommon (1c)
32. uncommon (1c)
33. uncommon (1c)
34. uncommon (1c)
35. uncommon (1c)
36. uncommon (1c)
37. uncommon (1c)
38. rare (2c)
39. uncommon (1c)
40. uncommon (1c)
41. rare (1v)
42. uncommon (1c)
43. rare (2c)
44. uncommon (1c)
45. rare (1v)
46. uncommon (1c)
47. uncommon (1c)
48. uncommon (1c)
49. uncommon (1c)
50. uncommon (1c)
51. uncommon (1c)
52. uncommon (1c)
53. uncommon (1c)
54. uncommon (1c)


Dungeon of the Forsaken
1. rare (2c)
2. rare (1v)
3. rare (1v)
4. rare (1v)
5. rare (2c)
6. rare (1v)
7. rare (1v)
8. rare (2c)
7. rare (2c)
8. rare (2c)
9. rare (1v)
10. rare (1v)

Nightfall Bandit Dungeon
1. rare (2c)
2. epic (4c)

The Lost Grove
Themed: 5/20

1. non-themed, epic (2v)
2. themed, rare (1v)
3. non-themed, epic (1v2c)
4. non-themed, epic (1v2c)
5. non-themed, epic (2v)
6. non-themed, epic (4c)
7. non-themed, epic (4c)
8. themed, rare (1v)
9. non-themed, epic (4c)
10. non-themed, epic (4c)
11. non-themed, epic (2v)
12. non-themed, epic (1v2c)
13. themed, rare (2c)
14. non-themed, epic (1v2c)
15. non-themed, epic (2v)
16. non-themed, epic (1v2c)
17. non-themed, epic (1v2c)
18. non-themed, epic (4c)
19. themed, rare (2c)
20. themed, rare (1v)

Aryth's Spire
1. rare (2c)

Nightfall Bandit Camp
1. rare (2c)

Fungus Grove
1. rare (2c)
2. rare (2c)
3. rare (2c)
4. rare (1v)

reserved