In places where prostitution is legal are prostitutes required to go through with it after taking money?

Yes. As the service is legal, normal law of contract applies and either the prostitute provides the service or gives the money back. The difficulty, as ever, with an unwritten contract is proving what it was actually a contract for in court if either side sues. If the sex was disappointing, there is no clause that it had to be of a certain quality, and how would you define that anyway? Plus it would be extremely embarrassing to actually take the matter to court, which is undoubtedly way you never hear of anyone doing that.

Related laws will vary by each location that has it legalized.

Generally speaking, I'd expect no one is forced to go through with it if they don't want to for any reason. Presumably somebody would simply get their money refunded.

What would be interesting is disputes over the quality of services after the fact. For example, if somebody pays $1000 for something, then says that the service was really bad and substandard, and they want a refund or else they'll sue over it. If it's something like a hairstylist, they can offer to redo it. Can you have a "redo" in a situation like this here, maybe with a different stylist? Can you sue for the pain and suffering of not getting it right the first time?

Yes, of course.

Being as this is the legal section I advise you call your lawyer

no but they have to give back the money