Might + present tense and could + present tense can be used to express a possibility of something in the present tense. May and can are present tense only.
@zerohedge is right, might sounds a bit more polite (when asking) than may, and both sound much more polite than can or could.
I may go to the park.
I might go to the park.
Can I go with Bobby?
Could I go with Bobby?
You could substitute any of the words in any of those sentences and say the same thing.
When might and could are used to express a past possibility that no longer applies now, might and could are always followed by have + past participle.
I might have gone to the park, but it was raining.
He could have gone with Bobby, but he ended up not going.
You cannot use can or may here, or might/could + present tense.
This answer is from a British perspective: I don't know whether the situation is similar in the US or other English speaking countries. It is necessary to consider the first question in two different contexts:
You are in somebody's home and they offer you tea and cakes.
Host: Will you be having cake?
Guest: Yes, thank you.
This is a polite offer, and only the first answer is suitable as a polite reply. The remaining answers would be much too assertive, though "Yes, I will, thanks" would be OK.
You are talking with a friend about your birthday party, which is next week.
Friend: Will you be having cake?
You: Yes, I will -or- Yes, I will be
This a request for information, and the first two I will answers are appropriate: they are examples of answer ellipsis.
The Thanks answer is not appropriate because the friend is not offering you cake.
Yes, I will do is an answer ellipsis of Yes, I will do that, or Yes, I will do so. It is probably not an appropriate answer to this particular question, but might be an appropriate way to accept a suggestion, for example:
Friend: I think you should buy a cake
You: Yes, I will do.
For the negative replies about cake, 1 and 4 are OK for offers of cake, and 2 and 3 are appropriate for requests for information.
For will you be late?, all of the positive and negative answers are appropriate, though "No, I will not" might sound a bit tetchy.
Best Answer
The premise of your question is wrong. This is because there is no future tense in English. We can refer to future time in many ways. One way is to use the simple present, as in:
1 Unless I see the money on my desk by tomorrow 9am, you're a dead man.
The modal will can also be used to refer to future time. This seems to be the construction you're asking about, so I'll bold an example:
2 Unless they will agree to paint the house red, do not hire them.
(It has been stated that "(this usage of will) is not exactly about the future; it's about volition, i.e. "will" (or willingness)." To which, I reply that as uttered by someone, I am not sure we can neatly cleave willingness and referring to future time. I will go with you is expressing one's present willingness to perform the stated action in the future). Even so, I offer another example:
3 Unless they'll go to see Star Wars tomorrow, I'm not going with them.
But so can about ten other constructions, including these common ones:
4 Unless I am seeing the money on my desk in five minutes, you're a dead man.
5 Unless you are going to tell me the real reason, don't bother to open your mouth.
6 I don't want to bother you for a ride to Boston, unless you'll be driving there anyway.
7 Unless you're about to leave, don't bother washing the car windows.
8 We're going to have way too much work to do unless you are to come to your senses and hire some temps.
(Granted the last construction {to be plus to} is rather stilted and part of 'old school' business language.)
Edited to add:
Other examples of present progressive to refer to future time:
9 Unless I'm sitting here and hearing the sound of your feet walking up the stairs to my office in five minutes, don't bother to come.
10 You can't have any unless you're doing your homework in five minutes.
Also note the response to the question Can I have some candy?:
11 No you may not. Not unless you're doing your homework in five minutes.*
Etc.