If somebody changes your Class during combat (such as with a Curse), does that change your combat bonuses?

Yes. If you quit being a Class, you can no longer get a bonus from Class-only items, and so on. You can never get the benefit of two Classes in one combat unless you have a special card that allows it. Exception: Abilities driven by discards work even if the Class with that ability is lost. If a Warrior had already discarded a card to get a +1 combat bonus, and then stopped being a Warrior, he would keep the bonus, but wouldn't be able to discard any more cards for the Warrior bonus. Yes, this rule can be used to the player's advantage. (However, you cannot discard a Class and play another copy of that card to use its abilities twice.)