Does it sound strange when you hear I don't hate ... instead of
I don't dislike ...? Or It's not strange instead of It's not uncommon, and nobody who rises late ... instead of nobody
who does not rise early...? Do they make difference?
It doesn't sound strange. There are differences in meaning. "I don't hate it" could mean "I might dislike it, but I don't hate it".
"Nobody who rises late" only rules out people who rise late, not people who rise on time. "Nobody who doesn't rise early" rules out people who rise on time, not just those who rise late. Of course, there is no exact definition of what it means to rise "on time", so that's more a difference of nuance, but "you must be an early riser" is a slightly stronger proposition than "you mustn't be a late riser".
Is there any case that the two negative elements in a double negation
sentence cancel out each other and turn out to be a pure positive
meaning? e.g. I don't disagree with that. → I agree with that.
"I don't disagree with that" doesn't necessarily mean "I agree with that". It might mean "I don't have an opinion on that" or "I'll assume for the moment that you're right about that". Sometimes, "I don't disagree with that" gives the listener the impression that you agree with them, while stopping just short of endorsing their point of view.
Similarly, if something is "not cold", it doesn't mean it's warm, and if it's "not long", it doesn't necessarily mean it's short (it could be a moderate length).
On the other hand, if you say to someone "You're not serious", you mean "You're joking" or "You're being humorous/wry/frivolous/silly" or something of that kind. The chances are small that you are telling someone that they aren't serious but that they aren't necessarily being silly or jokey either - but it's a possibility in principle.
Some things are generally taken to be binary. In most circumstances, if you say a whole number is "not even", it means it's an odd number. If you say a binary digit is "not one", it must be zero. Most of the time, if you say that something is "not true" or "not correct" or "not right", you mean that it is wrong, and people will understand it that way, but of course there is room in philosophy for discussions about whether something can be neither true nor false, and so on.
