1. Let him do what he will.
2. Let him do what he can.
(Are the sentences grammatical?)
3. She won't open the door.
(In this sentence, what does 'won't' mean? 4. She is not going to open the door. 5. She doesn't intend to open the door. Does #3 mean #4 or #5? I mean, is 'won't' in simple future or in volitional future?)
1 & 2 are both correct, but do not mean the same. "Can" means "able" as in "Let him do what he is able to do." "Will" means what he wants to do, or decides to do.
#3 means the same as #4 and #5. She is not going to open that door. It might be that she cannot (is not able to) or will not by volition, but it means all the same. That door isn't going to open if left to her to do it.