You have some issues right now that you need to resolve/fix/handle/deal with, so I don't think we should start dating anytime soon.
Are these interchangeable and equally natural? Which one do you prefer?
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In this context (dating) I think they all mean basically the same thing. There are subtle differences:
Again, in the context of not wanting to date someone, all of these words will get your point across. Personally, I would probably say "deal with" in most interpersonal situations of this nature.