You dont really need to use "will" in the first example as you have already said that it is something he does regularly by using "every day".The second example is how an English person would say it.
In this example "won't" and "wouldn't" are the same but "won't" sounds better.
If you give a reason - "wouldn't have" - sounds better - " Most people wouldn't have seen last night's lunar eclipse because they were working"
The difference with "Might/May not" is that it implies that you are not sure if those people saw it or not.
"I won't be going out tonight" - certain
"I might not go out tonight" - unsure.
Hope this help AlexAK