The Frog Icon represents the transformation spells, so yes, you can do that. The way to get the dove, crow, frog, squirrel, or bat avatars (or the mini spell) is by having someone fall asleep in a ring of mushrooms, then cast the spell on you. It's random, so you probably won't get what you are looking for the first cast.

It'll go away after some time, yes unless you save your deer as that animal. Whenever you wanna become that animal again, just go back into your list and click "Load Deer". c:

Edit: I believe...my deer is laying with yours in a mushroom circle xD

_ChainArt
Yeah, Remo and Aneirin were laying in one earlier XD Funny, that moment i was trying to get the spell to cast on you or one of the fawns.