So... when an egg hatches, you get the ability to help it or let it come out naturally. Is there a right or wrong way to help it...? Should you always do one or the other?
Just confused on this x.x

There is no wrong or right way to hatch an egg unless you let it sit without hatching it when it wants to for over 48 hours. Both ways give you bonuses the let egg hatch on its own is a stat bonus and the help egg hatch is a health bonus. I hope this answers your question.

Thank you! I was quite confused about what each did, I would only let them hatch on their own
This helps immensely, thank you

Your welcome.

on the popup,
> helping a hatchling gives it +20HP
> letting it hatch without help gives it +1 to any one of Str, Int, Dex, or Agi, at random
> Philter is obviously "select the philter you want from the dropdown"

Letting it hatch via being unattended for too long (so it hatches without use of the popup) means it gets no bonus at all