It can seem like a lot of work to learn about plumbing, but with some research and effort, you can educate yourself on the subject.
If you have a water pipe that freezes, turn on the tap to the faucet nearest the pipe so that the water has somewhere to exit as the pipe thaws. This reduces pressure to keep the pipe from bursting, and keeps it from bursting.
Do not pay anything until they finish the problem is fixed. You might have to give them a deposit, but you should never have to pay in full until after everything