Suppose that you are on a user's profile and start to answer a handful of their questions with little delay between those answers. Is this behaviour acceptable?
Will those answers get reversed, like upvotes after serial upvoting do?
There isn't, as far as I know, any script that would automatically reverse (whatever that would mean) serial answers. If those answers all got upvoted by the same user within a short period of time then, as Glorfindel notes, it's possible that the votes might get automatically reversed, but the answers themselves should still stay.
There's also no rule against answering multiple questions by the same user, if you indeed just legitimately stumble across them. However, having your friend post a bunch of easy questions for you to answer (and the two of you upvoting each other's posts) may count as a voting ring, which can be considered abuse of the site. And, of course, if your "friend" is actually imaginary, then it's abusive sockpuppetry, which is definitely not allowed.
Because legitimately answering a bunch of questions by the same user could look suspiciously like sockpuppeting or a voting ring, it's possible that doing so might get your behavior investigated by the mods, possibly after a well-meaning flag by some ordinary user who noticed the coincidence. Normally, it should be pretty easy for mods to tell legitimate "serial answering" apart from abusive voting rings or sockpuppetry, because in legitimate cases the accounts involved will have separate histories of legitimate interaction with other users on the site, and usually won't be posting at the same time from similar IP addresses.
That said, borderline cases can certainly sometimes come up, e.g. when multiple people taking the same class or working on the same project create accounts at the same time from the same network, and start asking and answering questions on the same narrow topic. In such cases, it could be hard for mods to tell whether the interaction between the accounts is really legitimate or an attempt to game the site for quick rep. At worst, this might lead to some or all of the accounts involved getting suspended or deleted.
(For example, here's a random case of suspected sockpuppetry where the user(s) involved apparently claimed to be siblings. Based on the fact that the accounts were deleted, apparently their behavior was deemed in the end to be abusive sockpuppetry. The plagiarism involved certainly didn't help their case.)
In the unlikely case that this happens to you (and you're not actually sockpuppeting, of course), you should be able to appeal the decision e.g. by contacting SE staff. However, the best way to avoid such suspicions in the first place is to avoid voting on posts by your friends, siblings, classmates, coworkers or other people you know outside Stack Exchange. Just answering their questions is still fine, though — after all, even answering your own questions is explicitly allowed. Just don't upvote their questions or answers yourself.
There's no issue with this at all. If that user happens to have a couple of questions on a niche subject, and you're one of the few people with knowledge of it, by all means, go for it.
There could be some trouble when that user visits the site, sees a handful of answers on their questions and starts to upvote them all. The serial voting reversal script is likely to kick in and revert those votes. But I don't recall an instance where a 'serial answerer' got 'serially upvoted' by accident – in most cases, a single helpful answer by user A on a question by a new user B causes user B to upvote a number of posts by user A, not just the answers to B's own questions.
Yes this is absolutely fine, and I've done it in the past. It can be an alternative to listening to various tags. The quality of a Q & A site only increases with the number of good answers.
You might want to refrain from upvoting the questions though when you are answering: a good rule of thumb is to never use the voting buttons on a question or answer that you've arrived at via a profile page.