When you hatch you have a 50-50 chance of getting one of the two pets so if you did hatch dark sprite with satyr you may get satyr or just another dark sprite.
Hybrids are special pets and only are made when you hatch a school pet or some promotional pets with other school or promotional pets.
If you did hatch the dark sprite with the satyr I don't think your sprite will have the satyr card but the talents the satyr would give have a chance of getting to the dark sprite. Plus your new dark sprite would have a higher pedigree.
Hatching is kind of hard to understand at points and to be honest the best way to learn is try it out for yourself.
In answer to your questions in order, No, No, No, Yes.
A regular life only school Satyr can't be hatched to another player, it is a school specific pet that is only obtained from that school teacher, but the person with the Satyr pet can get it as a result of the hatch if they don't get the potential hybrid.
No it is not possible to have pets switch cards, you will always get the card of the dominant parent-what it looks like-but you can manipulate the stats and talents via hatching and training.
Hybrid percent is low to mix between pets that may produce a hybrid.
If you hatch with a hybrid pet, you do have a chance of getting that hybrid pet as a result.
