Yeah, everything bur Horn carries over. Anything white on evolved forms can also be used on previous forms, so learning Cornered Beast on Behemonster allows you to use it on Babybehemoth.
As Nep says, you'll have enough to get all medals + do all interventions, near the end of the game, the game shits out a bunch of gems anyway to the point where you'll have some left over. I personally prefer doing all interventions first before buying a bunch of medals, I only bought useful medals or medals of heroes' themes I wanted for battle. I really loved how they made each medal give a different battle theme.
No clue if its possible, probably could be with a ton of grinding in nebula cave, as no other area gives as much exp as it does before then.