Let me try to keep it simple:
Zapamiętać vs popamiętać - I agree here with the explanations below but I would like to add some comments from the practical perspective:
*Zapamiętać - it means remember and it's similar to pamiętać but you use ZApamiętać when you want to kind of underline the moment that something has/will become a part of your memory and now you simply remember it.
ZApamięTYWAĆ is used to underline process/phase of memorizing which is still in progress.
@Doyeop your understanding in terms of culmination is correct.
It's similar to kochać/zakochać/zakochiwać, where:
Kochać - to love, in general, constantly.
Zakochać - to fell in love, to underline that it happened and now you're in love with somebody/something, but it also can happen in the future because here it's about this critical moment between not being and being in loved.
Zakochiwać - as above but stil in process of felling in love.
@Dave, as you can see using "ZA"kochałem się is indeed past form but it still means you love, it's basically the same with "pokochałem" - unless there is clear context in the story and people know that you do not love sb/smth anymore.
*Popamiętać - in general as a verb itself refers to an unpleasant situation but it's rather used in the context of revenge or threat against the people who were the co-creators of this negative experience.
You can still hear sometimes "jeszcze mnie popamiętasz (popamiętają) " which we can translate as "You'll remember me", "You're going to be in trouble (one day)" / "I will take revenge, you'll see".
This is how I use these two words.