Hard to tell for sure--was the broken link the one with the joining pin in it? That would be telling. The probability of the chain breaking in a short period of time under what sounds like modest load elsewhere is low. If the link came apart it could jam in the derailleur and the force could pull on it. Mistakes happen but the shop has control of how they handle this. Give them the chance to make this right--they have an opportunity to prove to you how they stand by their work and their standards for service.
Mechanically, I would carefully bring the hanger closer to sanely straight with knipex wrench pliars so as to not too much force on the hanger threads before aligning it with a hanger alignment tool. It'll probably be mechanically OK, although the paint on the hanger will likely be a bit messed up, and there's a small chance that it will break. If it comes back straight it'l be fine for use, though the odds of it braking if it gets bent again are much higher than before. Obviously new derailleur and chain.