Your first explanation comes closest.
The definition online for this form of would is:
- (expressing the conditional mood) indicating the consequence of an imagined event or situation.
So there's an element of the hypothetical involved. "He will do it" communicates too much certainty, whereas "he would" is dependent on something else having happened. Even if the person is communicating "he would" because "it's part of who he is", there would still need to be some kind of trigger or set of circumstances under which the person "would" carry out the specified behaviour. "He will", on the other hand, suggests that it's actually going to happen.
2) He will do it (if some conditions are met, but now those conditions are not met , Probably I won't do it anymore)
This one would be incorrect, as there is no implication that he won't/wouldn't do it any more.
3) Part of reported speech in some article. For example He said "He will do it" or future in the past
This seems more to do with the context than a specific meaning of the phrase? (I'm struggling to make sense of it.)
4) past habit
This one is correct, though I feel it would usually be contextualised in some way, e.g.:
He would go for a walk in the park every once in a while.