Nope
As far as we can tell the pre-gen characters can't be customised much if at all, but I think they're planning on compensating for that a bit by having the Backgrounds system actually come up in the story too, so, entirely custom characters have a bit more detail too them though not quite on the level of the pre-gens
very little customisation except class I think
nope, Origin characters/companions have fixed classes. Just like in the originals.
In the original DOS you can customise. Didn't they change the vampire spawn's class during the origin story?
Dos 2 didn't even have classes, in BG3 all Origins have a fixed class,Wyll (Human Warlock), Shadowheart (Half-elf Cleric), Lae'zel (Githyanki Fighter), Gale (Human Wizard) or Astarion (Elven Vampire Spawn, Rogue) like Vicconia started as a cleric or Minsc as a ranger.