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?)

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. Yes, "Let's play tennis, shall we?" is grammatically correct. It is an invitation to play tennis and the tag question "shall we?" is used to seek agreement or confirmation from the listener.

2. "Let's not play tennis, shall we?" is also grammatically correct. It is an invitation to refrain from playing tennis and the tag question "shall we?" is used to seek agreement or confirmation from the listener.

3. "Let us play tennis, shall we?" is grammatically correct. It is a more formal way of extending the invitation to play tennis, using the pronoun "us" instead of the contraction "let's." The tag question "shall we?" seeks agreement or confirmation from the listener.

4. "Have a cup of coffee, will you?" is grammatically correct. It is an invitation to have a cup of coffee, and the tag question "will you?" is used to ask the listener to comply with the request.

5. "Have a cup of coffee, won't you?" is also grammatically correct. It is an invitation to have a cup of coffee, and the tag question "won't you?" is used to ask the listener to consider accepting the invitation or to prompt a response.

The difference between "will you?" and "won't you?" lies in the expected response. "Will you?" generally expects a positive response, while "won't you?" generally expects a negative or hesitant response.

1. Yes, the tag question "shall we?" is grammatically correct and commonly used in this context. It is a way of inviting someone to play tennis together.

2. Technically, the tag question "shall we?" is grammatically correct in this context, but it may sound a bit unusual because it is generally used to suggest an activity rather than to discourage it. However, the overall meaning of the sentence will be understood.

3. The tag question "shall we?" in this context is grammatically correct and expresses a suggestion or invitation to play tennis together. It has a similar meaning to the first example.

4. The tag question "will you?" is commonly used to make a polite or casual request for someone to have a cup of coffee. It is grammatically correct and typically implies a positive response is expected.

5. The tag question "won't you?" is less commonly used in this context. While it is grammatically correct, it can give a slightly different tone. It may imply an expectation or assumption that the person will decline the offer, or it can be used as a rhetorical question when you already know they won't have coffee.