Once you've finished

Answer 3 is almost equally good here, with little to choose between them. The verb must be Passive, however ~ which rules out Answer 4 ~ and meanwhile, No.1 also contains a false participle.

The emphasis, at this next stage, is that the parents (and the house!) can't really 'breathe' until AFTER the children have all moved out: there is a real sense of needing a Perfect ('have') element in the sentence, in order to be able to move beyond that.
Answer 1 would not be wrong, but No.2 captures the sense of time better. 'Go' (while certainly better than nothing) is not the best verb here, so Answers 3 & 4 are weak.

Although, in this situation, the overall sense of the first clause is clearly Future Perfect, English speakers very often simply use the Present (leaving the rest of the sentence to express the timescale more accurately). None of the auxiliaries offered in Answers 2-4 would be suitable here.

The letter-writer 'has been using' the product over a considerable span of past time; and either he still is using it, or perhaps the rest of his letter (which we'll spare you) would go on to explain why he has now discontinued the habit of a lifetime.
Each of the other versions would be understood, and Answer 1 is an alternative possibility (except that it lacks any emphasis on the cumulative continuity), but none is as cogent as No.4.

Once again we are 'looking back' on what has already been achieved by a certain time-point: in this case, that the child 'will have' grown that much hair.
(A typical human scalp contains up to 120,000 follicles, each growing up to 1cm/month, which yields an annual total of almost 15km; multiply that by 11 years, and you have 100 miles or so of hair!)
Meanwhle, the tenses in Answers 1 & 2 are understandable but wrong; there was no need for a Conditional in Answer 4.

We need the Future Perfect here, and perhaps also in its continuous form, to emphasise that the young person has been doing this for over 10 years (since age 5, at least; for an hour a day, 5 days per week over almost 40 weeks per year; plus homework, and any 'incidental' maths in other subjects such as Science and Geography) ... and would probably struggle to remember a time in their life before that had begun.
Answer 3 is far from bad, but with less of this nuance than No.2; the two outer Answers are also possible, but No.1 assumes an individual who has already reached GCSE (rather than being somewhere along the way towards it), while No.4 suggests ~ in rather formal, even prescriptive tones ~ that a child who has not yet turned 5 years old will definitely 'have it coming to them' whether they fancy it or not!
Incidentally, nobody is pretending that all those 2,000+ hours are actually geared towards two 90-minute Papers as a final target. Maths is far broader and more important than that!

'Finish' is the most obvious everyday verb in this context (in the sense of 'finishing reading/writing/answering them'), so Answers 1 & 2 do not read fully naturally. The usage of the simple past with 'just' in Answer 3 is typically North American.
Answer 4 may seem bulky, but the initial elision helps soften that slightly. The ongoing process of dealing with the messages (which, so Stephanie herself would probably argue, 'takes as long as it takes') justifies the use of the continuous form. She has now completed her messages, and is able to come out and attend to other things at last!

Answer 4 is the best here, despite its two contrasting uses of 'have'. The first one, again, whisks us forward a few years to a time by when some grandchildren will HAVE been born. But the families may still (by then) be incomplete, and in ongoing process of active enlargement ~ hence the need for a Continuous form. The 'having', at the end of the phrase, is a slightly sloppy but widespread use in the sense of 'creating / giving birth to / bringing-up / 'owning' ' children. We could almost as easily have used the phrase 'starting a family', but then, one can only 'start starting' once rather than with repeated additions. This is partly why Answer 2 does not work very well, despite its intended meaning being reasonably clear.

The verb 'be' cannot comfortably form its own continuous tense (although the participle 'being' most certainly exists), so Answer 1 will not suit; Answer 3 contains no element of the Perfect (even if you are reading this after it happens, if it does/did; it is being written around the turn of 2014); and Answer 4 uses the simplistic 'foreign' logic that if indeed she still is there, the verb ought to be in the Present (as in French, German and many other languages; but that isn't how we phrase such things in English).
So we are left with Answer 2!

Answer 1 would be a fair alternative here; but again, the sense is that the choices can only follow once the move is complete, for which a Perfect verb-form is simple to use and clearer as to meaning.
Answer 2 is an unnatural way of forming a future continuous, and the continuous element is inappropriate here anyway; the passive voice in Answer 4 (though understandable) is also inappropriate.