Hopefully it will be a simple answer, I have a farmed pet leveled to ancient for the card gained, but have found all abilities gain where bonus to its stats.
if I decide to hatch it, what is the probability that it will still retain these undesired traits in generations following? should I farm for a new one, hope its trait will be better, or just hatch 15 generations until they are gone?
From my experience, a pet will inherit half of each parent's talents - 5 from each. However, those 5 are RANDOM, so you can easily inherit 5 of the non-manifested talents.
Also, keep in mind that you only have about 40% chance of getting the talents you want - seeing as the pet will only manifest 4 out of 10 talents. Your best bet, if you got useless talents, is to hatch the pet and train the offspring.
My experience (limited as it is) may illustrate what you can expect with hatching a low level pet to improve its talents.
My Life wizard has the Brown Spider because it provides a +25% damage-enhancing "bubble" spell for all Life damage spells. Yet it's a "Death" pet with boosts to Death accuracy, damage, etc. Aside from the great card, the pet is otherwise useless to my Life wizard. So, I bred the spider with her Satyr.
The first generation cross-breed was still a Brown Spider. It still manifested the +25% damage to all Life damage spells card at ancient. However, now it only expressed one of its former talents, plus three from the Satyr (although considerably weaker than in the Satyr). The new Brown Spider was still a "Death" pet, but it's stronger over all. Best of all, it now has two useful talents (but rather weak), one good "selfish" talent (because it boosts the other two useful talents) and only one useless talent.
I also noticed that the baby pet only inherited talents that were already known and expressed in at least one of the parents. It didn't inherit any "new" talents that I hadn't seen expressed already (through training). If both pets are mostly untrained, the inheritance may be random. But, when both pets are fully trained, it seems the talents that appear in the baby will most certainly be talents already known and expressed in the parents.
I haven't tried cross-breeding my second generation spider yet due to lack of gold. I can't promise that repeated cross-breeding will retain the spell card you want. But at least with the first try, the baby seems to keep the weaker parent's appearance and spell card, while gaining new/better talents and overall strength from the stronger parent.
It was kind of fun to try, but very expensive. Choose the second parent very carefully, and try to pick the most powerful, desirable parent you can find.