Park & Fly is nothing more than a lot near the airport that you won't get towed away from. The fence around keeps people from driving out without paying. Oh, they give you rides, but they won't guarantee they'll actually do that quickly, even if four buses drive past the shelter you are standing in. Security isn't included in the price. The valet lots might be more secure, don't know.

This damage is for your own insurance to resolve. Same as if you parked on a street. The city won't cover any theft or damage to your vehicle.