1. The door won't open.

Question

2. She won't open the door.
(Does 'won't' mean 'volition' of the subject? Or does each sentence have a simple future tense?)

3. She will open the door.
3-1. She intends to open the door.
3-2. She is going to open the door.
(Does #3 mean #4 or #5? Simple future tense or volition?)

4. She shall open the door.
5. I will have her open the door.
6. I will let her open the door.
7. I will make her open the door.
(What does #4 mean, #5, #6 or #7)

Answer 1

1 is simply future tense.
2 involves volition (she refuses to), yes.

3 is simply future tense.
3-1 states volition in "intends"
3-2 is simply future in sense.

4, 5, and 7, have the implication of "forced to" in them.

6 has the idea of being allowed to, but not forced to.