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!
Since English doesn't have a future tense, somebody has to do it.
Will and shall are auxillary verbs that are used, among other things, to refer to future time. They attach to the noun as 'll.
Regarding your questions:
It is grammatical.
It is covered in textbooks (example).
Yes, you can say:
Then you call me and tell me where you are and I'll join you.
Strictly speaking I'll join you is not using a future tense.
Best Answer
I've got something to say is fine.
HAVE got can be used almost anywhere that bare HAVE is used as a "lexical" verb—that is, as a main verb rather than a perfect auxiliary. It can also replace HAVE in the "periphrastic modal" HAVE to = 'must', as in "I've got to get a haircut."
The principal restriction on HAVE got is that it can be used only with HAVE in the simple present form: I/you/we/they have got, he/she/it/John has got. It can't be cast in the past-tense form, or the progressive construction, or in the infinitive or participial form.
There are marked differences in BrE and AmE use. In AmE HAVE got is largely restricted to conversational situations, probably because it was for a long time deprecated as vulgar by US English teachers. It is acceptable in all registers in BrE.
In BrE HAVE got is routinely used in questions and negations:
This is rare in AmE; US speakers tend to revert to the ordinary HAVE in these contexts:
The distinction may be attributable to the AmE preference for gotten as the past participle of get, where BrE speakers prefer got: BrE treat HAVE got as a sort of idiomatized perfect. This analysis is supported by the fact that ain't got is fairly ordinary, and by the growing frequency of bare got, without the HAVE, in AmE:
Colloquial AmE, it appears, is coming to regard got as the core of the expression and HAVE as a dispensable ornament.
The descriptions of AmE use rest on my own analysis of the UCSB corpus of spoken English. In conversational contexts I found 545 instances of indicative have/has and 158 instances of DO have, against 171 instances of HAVE got, all indicative, and 90 instances of bare got. In non-conversational contexts I found 167 instance of have/has/DO have and only 4 instances of HAVE got.