1) Generally any changes from one A to the next A will be very minor, like maybe a few pickup notes or some bit of transition. If your form starts with AA then generally this means repeating the first section. More noticeable changes but where you keep the thematic material you can indicate with a prime: AA'
So changing the melody generally, given how most people think of these things, would introduce a new section.
A key change where you keep all the material the same (but transposed) is interesting. I think one could justify a prime marking here (AA') but it kind of depends on how long you stay in the new key and how you get there.
2) No, changing key in a section doesn't automatically mean you have a new section. You might think of it as a subsection if that helps you with the structure but you don't have to. Sometimes we shift tonality briefly but then quickly return to our home key, no need for a new section for these brief forays.
Quite often key changes do accompany new thematic material so you would have a structural point but it doesn't have to be this way.
3) You can extend form in any manner you choose. AA', AB, ABA, ABA', ABCA, ABACA, ABABCA, ABCDCA, AABABCBA, and so on and so on and so on.
4) If you are writing for a genre that has some well-established forms then it is a very good idea to be aware of them and use them. At the same time it behoves you to be thinking of ways to play with those established forms. That little bit of novelty can be what gives a piece that extra magic that turns it into a hit. You play with people's expectations and sometimes people like that.
Unfortunately I don't have examples of any of this.