1a) Not everyone, some people should be falling. I'd say only races with the ability to fly, flying spells, or features that grant flying should allow a character to fly, if flying is properly implemented. Otherwise the character would fall and thus be a target for something like Feather Fall.
1b) I could have read your explanation wrong and instead you are saying everyone who flies should be always flying at a height of 20 feet in the air, to which again I would say no. Some creatures innately fly like an Imp or Raven, and not every dungeon has a headspace of 20 feet. Furthermore, just setting all flying creatures to 20 feet in the air would be a headache for actually controlling and interacting with things, and would be a headache in combat.
2) No, unless more verticality is added, no. And even then it should only be that they can not be targeted if they are out of the range of a melee attack. Just making flying creatures immune would be hell on balance and honestly kinda unfun. Even in base 5e flying creatures typically will swoop down into melee range for their attacks unless they too have a ranged weapon or spell, but those kinds are usually at a higher level when a party has enough ranged tools to deal with them.
3) That's already a thing I think. I might be remembering the BG3 implementation but I think it matches 5e in that a flying creature is not touching the ground so it is not affected by terrain. And I think flying creatures such as a raven familiar already show to be immune to terrain effects.
4) IDK.
Otherwise, I do think flying only amounting to a unique jump is a little eh, especially since it seems to break opportunity attacks and such. However, I am unsure how it should be properly implemented. Adding an entire 3d space of verticality for characters to rise and fall with flying is likely beyond the scope of this game. But I do want flying to be a bit more than a pseudo jump or teleport, but it could be beyond BG3 for that so I can be content with the current implementation.
