Yes, it's correct. It's slightly 'wordy' though. If I were you I'd neaten it up by getting rid of the vague term 'they', and making 'your city' the subject: What river does your city get its water supply from?

Your sentence is fine. Good job! (Some water supplies are not from rivers. Some are from mountains or underground streams. In that case, you could ask, "What is the source of the water supply in your city?")

Your sentence is fine!

Yes.

Some people who are particular about grammar would say the better sentence would be: "In you city, from what river do they get the water supply." But your sentence is completely natural sounding.