@Vaxl
The dominance of a trait corresponds with the trait itself. So for example, wings will always be dominant to flames, regardless of gender or even carried vs. visible. I'll be adding a section covering this eventually!

As for whether a wf and a Nf could produce an ff baby, I haven't tested that thoroughly enough to give you a definite answer. From what I've noticed so far though, it seems that the baby would end up displaying wings and never flames.

@Bella
This one is tricky since we can't actually see which alleles or carried in the same slot. I'd need to do a lot of further research before I can conclude whether the breeding has actually changed the genotype. Hopefully we'll get that figured out sometime!

@Kaosu
Thanks for the link, it's very valuable! Eventually when I make a section for the guide covering the inheritance of colour, I'll definitely include that link. That said, I can assure you the generator will display in-between colours sometimes! You just have to keep clicking that test button. I know I've seen it tons of times for some breeding projects of my own.
One thing to keep in mind is that the colour mixing operates according to additive colour, not subtractive colour.

I'm just going to re-post my question because it seems to have been missed: Do the stats of the parents effect that stats of the child?

Sorry about that!
Yes they do, as has been confirmed by admins. I'm not sure myself as to how this works exactly, other than that the stat boosts received from hatching are cumulative through generations.

Update:
I have recently discovered, after hatching this offspring that recessive alleles can be passed down, even when paired with a dominant! It is simply a rare occurence. Hurray, science!

@Reynbowz
Actually, that doesn't prove that a recessive allele could be passed to offspring, since the recessive is not competing with the dominant. Basically, the offspring have a 25% chance of carrying the recessive allele and a 25% of carrying the dominant. If the gnarled horn was visible rather then carrying, and a parent of gnarled horn was unicorn horn, and the offspring was carrying unicorn horn, that would prove the carrying recessive allele hypothesis.

Also, I've been playing with spirit flames and butterfly wings in the breeding grounds and it seems that dominant traits exert incomplete dominance- what I mean is, sometimes the recessive can still get through. Has anyone else found this?

Lastly, I found that I can't breed offspring back to parents (as is normally done in live animal breeding). Is this a glitch or intentional? Can siblings breed?

This question was asked in the Newbie FAQ and apparently parents and children cannot breed, and siblings cannot breed. That answer came from Krin :3

@Kauso
Fudgicles on a stick! That is going to make this much more tricky. Thank you, though, for clearing that up for me.

Here's what I've gathered about dominant and recessive alleles.

I have an interesting specimen: http://www.sylestia.com/view/pets/?petid=40601
Both parents have visible zebra stripes, but still, he shows leopard spots. If Z is the dominant gene and l the recessive, it means that two Zl parents can have an ll parents.
By extension, and also testing with the breeding grounds using tested parents, a Zl and a Nl can produce an offspring showing leopard spots..
The probability of these outcomes are determined by the genotype of the parents, one gene from one parent having one chance on two of being passed on.

In the cases I'll present, D is dominant, r is recessive and N is nothing. N>D>r, DD and Dr both show the dominant trait, rr shows the recessive trait, Nr and ND all show nothing

DD&Dr: 50% DD, 50% Dr
Dr&Dr: 25% DD, 50% Dr and 25% rr
Dr&rr: 50% Dr and 50% rr
Dr&Nr: 25%ND, 25% Nr, 25% Dr, 25% rr

So, in the case of a zolnixi showing wings and carrying flames breeding with another zolnixi that only carry flames, there is four possibilities with equal chance of occurring; the offspring:
A: carry flames
B: carry wings
C: show wings and carry flames
D: show flames

Also, there is something Krinadon said that bugs me a little: if the breeding system follow Mendelian rules of inheritances, a sylesti carrying a gene breeding with a sylesti carrying no gene at all would produce a carrier offspring 50% of the time. The carrier of the gene would pass on his gene half of the time and half the time gives nothing, while the other would not pass down any gene.

Can half siblings breed? Can a 3rd gen offspring breed with its grandparents?

Yes to both