The two sentences do have very similar meanings, and are interchangeable, but there is a slight difference in implication.
I might work more this week. Implies that you have control over the situation, however
I might be working more this week. Simply implies that you don't really have control or choice.
Your second set of questions, both make sense. However I would have said "I have to work more today" to show that I have to do it, not that I really want to do it.