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They could all be used, but the contexts would differ.
1. Will you visit me next year? Invitation
2. Do you visit me next year? If, say, you spend one Christkmas at one house and then the person comes to you, you could use this question to check whose turn it is
3. Are you visiting me next year? Have the plans and arrangements been made?
4. Are you going to visit me next year? Is that what you intend to to do instead of going somewhere else?
a lot of questions 
Linear Mode
