They're all correct. "Take a guess" is mainly used in North America, while "have a guess" is the standard expression in countries where British English is spoken. "Make a guess" is possible, but unusual.

I would use "take a guess". For example, I might ask a friend, "would you like to take a guess". I would also say "I'll take a guess". Some people might also say "I'll hazard a guess", which means they will volunteer or risk guessing the answer. Hope this helps

It really depends on the context in which your using it, however I'd say the most natural way to say it is 'take a guess'. People also say 'my guess is'.