This is why the linguists insist that English has two tenses: past and non-past!
These uses of what we ordinarily call “present” tense, simple or progressive, with future reference (instead of the explicitly futurive will) tend to be restricted to definite plans. They say in effect “This is what is on my schedule”.
Q: Sherry, is Bob free sometime tomorrow for a quick review?
A: Let me look at the book ... He’s in meetings til noon, and he’s out for lunch, but he can see you at three?
So sentences 1 and 2 are both acceptable, and there's no real difference between them. Discourse context will contribute to determining which you use (or whether you use will), but there's no rule you must follow.
Similarly, your final example, ‘But what do you do next year?’ I asked. ‘Yes. That is the problem,’ he replied is pretty ordinary. Questions of this sort arise, typically, when someone has described an action to be taken in the present or near future and you want to know what action will be taken in the longer term to account for the first action’s consequences. In effect, it asks “Do you have a plan for next year?”
The two questions, 3 and 4, are a bit different, because the phrase every day establishes a different sort of context for use of “present” forms. As you know, these forms are ordinarily used to describe habitual and repeated actions; every day reinforces that interpretation, and collides with a futurive reference. So these sentences are very unnatural. You might just get away with 3, Do you know what you are doing every day this summer?, if you are trying to find out if your interlocutor's calendar is fully booked. But I cannot imagine a context in which 4 would be natural; it suits better with a present referenc, something like this:
Do you know what you do every day? You leave the cap off the toothpaste every goddamn day!
Just a remark, as I have heard non-native speakers get this wrong. We can, and indeed often do, use the present tense to describe the future. However, when we do this, it suggests that the event being described has already been planned.
For example,
"My son starts kindergarten next year." That makes sense, because he's 4 years old. When he's five, he will be in kindergarten.
On the other hand, "OK, we're out of time, I have to go, we finish this conversation tomorrow" is NOT grammatical. This is something non-native speakers say a lot, but that strikes me as wrong. You must say "we'll" here. Does this distinction make sense?
Best Answer
I would like to add that "my brother is getting a degree" is a temporary situation, usually lasting a few years and that is why the present continuous is required. The present simple is used for permanent situations.