All are OK. I'd phrase #2 differently, but it's not incorrect as you've written it.
4 an 5 are basically saying the same thing.
1. Let's play tennis, shall we?
2. Let's not play tennis, shall we?
3. Let us play tennis, shall we?
(Are the tag questions all grammatical?)
4. Have a cup of coffee, will you?
5. Have a cup of coffee, won't you?
(Ae both okay? What is the difference between them?)
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