Learn English – Verb forms -s -ing (future tense)

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!

This is mainly a joke. There isn't a real tense in English to say "something that would’ve happened in the future of a past that was affected by something from the future," probably because no one has ever encountered such a situation. There's no grammatically correct way to combine tenses in this way.

If I had to make an actual "correct" sentence for this, I would say something like, "But it wasn't until his 21st birthday that 1955 Biff would have placed his first bet in that timeline." But again, there aren't really any rules in grammar about how to talk about time travel. If there were, maybe we had will could have used them.