Do enemies level up as your level increases???

Yes, through out the whole game. It keeps the game balanced. Even if you go back to a battlefield that was early in the game, the enemies will be around the same level as you.

Ahh, one thing I don't know is... Do they level up with Ramza, or with whomever has the highest level in your party??? I never got around to figuring that out cuz usually i have ramza at 40 when everyone else is at, say, 15-20 O_o (abusing the Yell ability of course...)

Random battle enemies will have levels near your highest-levelled unit.

Storyline battle enemies' levels are pretty much set. You'll only sometimes see them levelling up with you (like the battle in Sweegy Woods, for example). It seems that storyline enemies will level up with you if the enemy party is made of monsters.....