1) '됐어요?' means 'Are you done?' or 'Is it done?' in my perspective, and it's definitely a verb.
2) '-서' means 'Due to', 'Because', 'Because of', 'Since' in many ways. For example, you could say like "부족해서 못했어" for "Due to shortage, I(or whoever it be) couldn't". However, it would be much easier to understand it if you just take 'to' in your example as '-서'.