What Should I Do?

Belts dont just break it was either old an dryrotted when he installed it or he damaged the belt during install he is trying to get out of liability i would demand he fix it if not him the belt maker i would def see it through that someone has to take care of it

Don't let him take advantage of you, either he installed the belt incorrectly or it was a faulty or old belt, talk to the manager of whatever shop you took it to and make him replace it

Yep sounds like you need head work now due to bent valves. Not going to be easy getting it repaired at shops expense. Might be hard to prove he did anything wrong during installation and most shops only warranty their work not the parts that they use. Investigate what caused the failure. Was it a non name brand belt? Does that manufacturer have a warranty on the belt? Are their others that have had same issue with that brand? Is their a judgement active or bending against them for this same issue? Are all the mechanical parts that the shop might have touched or removed still attached like they should be or are some missing or loose? Could that have caused the failure? I don't envy you for the battle you have on your hands. Good luck and I hope it comes out in your favor.