1. Yes, they can turn into any animal, even extinct ones, that existed in their world. Also yes to mythical creatures not explored in our bestiary, though it would be more cosmetic, since powers/abilities of the mythical creatures need to have been witnessed to be used (Hollywood doesn't count).

2. Similar to the speech answer, because their entire perception of the world and instincts are different, it would have to be reawakened and relearned through practice and becoming skilled in their new magic.

Heck yeah tame horses!