Learn English – “Had” for future time

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!

Using the present tense for future events indicates certainty, consistency, and familiarity. In other words, use this to talk about events which will happen, which happen on a regular basis (or are predictable in some way), and about which you have some personal knowledge.

The holidays start next week.

I know this happens every year, last year I saw it happen in the same way, and I am sure it will happen the same way this year.

The train leaves in five minutes

I know the train leaves at a specific time, I know that trains usually leave on time, and I have seen the schedule to confirm when the train will leave.

The gala event starts tomorrow

I have personal knowledge that it is scheduled for tomorrow, I know that events like this usually start on schedule, and I feel comfortable asserting that it will definitely happen.

If any of these three does not exist, there is uncertainty, and the future tense will be more appropriate.

We get paid on Friday

I know this happens with some consistency and regularity, as I've already received at least one paycheck on Friday.

We will get paid on Friday

Oops, now there is some doubt. I hope this will happen, but I'm not sure it'll happen.

Here's another example: given no other context, consider these two sentences:

He will make the winning shot of the game in twenty seconds.

He makes the winning shot of the game in twenty seconds.

The first indicates a future condition, but the context is unclear. Do I really know this will happen? Probably not. More likely I'm expressing an opinion, or a personal hope.

But the second sentence, that expresses an odd certainty. The context is either that we are watching a recording of the game which I have seen before, or that I'm psychic, and I've already seen this happen with my mental powers.