I apologize if this question was already asked and answered but does the level of the parents affect the stats of the baby? Higher leveled pets breed babies with higher stats? Not talking about genes but the stats themselves.

Pretty sure they do, or at least, my foals seem to be decent with high stats here and there compared to a pair that are level 1.

The only level effect is Genetic Power which gives +10 to all characteristics for each grade. You can read about the rules of acquiring and inheriting of Genetic Power in FAQ.