You lose MP from damage dealt. 1/2 the HP damage also damages MP. And the way combat works, it's possible for a character with a defense of a million to still roll a 1 on his defense check, allowing the attacker to deal lots of damage.
The way it appers to work is this: You roll 1d(Strength) and 1d(Defense), then take the first roll and subtract the second. That gives you the damage dealt. So, it's quite possible for a super high strength to deal nothing and a low defense to block it all. Half of the damage also takes away MP, but you can still use spells even without MP for some reason.
I'm not sure what selecting the skills does though. Perhaps they are two different pre-generated dicerolls, so you pick one?