Emphasis. If you contract to "n't" you can't stress the pronunciation very easily. So people sometimes choose "not" to vary the tone/stress to make it stand out. "Have you NOT been there? I thought everybody who lives in Moscow has visited Red Square, and you've lived in Moscow all your life." (I put it capitals here, but the meaning would be conveyed by the tone/stress of the way it is said)

I could be wrong about this but, from a UK perspective, "Have you not been there?" and "Do you not like it?" sound like regional variants. To me, these constructions sound more typical of speakers from northern England and Scotland, as opposed to the more 'standard' speech of southern England. I know that you have friends from the north of England, so I'm wondering if you've picked up these speech patterns from them.

Both ways are correct. Both ways have the same meaning. But the first two sentences, the ones without the contractions, sound a bit stiff and less natural for everyday spoken English, although totally fine and grammatically correct.

To me, no difference in tone. Using "haven't/don't" is a bit more informal, but I would still say it to my boss at work. I think it's just personal preference, maybe some geographic differences between English speakers.

Thank you Clare!