Why stop at when the story is just beginning again for the first time?
Threepio was mind-wiped, so he wouldn't remember and it wasn't like Vader shared a room with him him much (much less willingly talks about his past). (In Legends, there was the "Thank the Maker" comic story, though.) The only sticky questions, IMHO, are if Artoo should've recognized Ben Kenobi or Yoda when first meeting them; the former I think is written in a way that it can fit, if only just. As far as Yoda goes, I don't recall him and Artoo having much contact during the prequels.
I find the X-Men movies did it worse, since it's really hard to imagine Victor Creed and Sabretooth being the same person even beyond the fact that the two actors looked nothing alike. IMHO, if we were to assume that they were the same character and overlook the differences, Logan's amnesia would explain why he doesn't recall anything and X1 Sabretooth is so quiet that there's nothing to preclude him knowing who Logan is. His extra interest in Logan during that movie makes more sense with a backstory like in Origins then if it's just a random new mutant where we don't know where he comes from or what his beef is.
I think the teams working on the movies not being up to scratch had more to do with it then anything else.
Nope. The Poe Dameron comics do show something similar for him, but Threepio's erased prequel memories are gone. The "Phantom Limb" one-shot comic not only confirms that one, but also offers some interesting insights to droid mind wipes.
Always thought they should've gone with a Force impression, like how we learn in ESB that it's possible to see "many things" through it, like "old friends long gone" or something like that.
I think the lack of aging in the First Class cast should be just chalked up to the age of the actors and left at that. In the case of Star Wars, the only real thing that stands out is that Ben Kenobi looks a good deal older then he would've been from the prequels due to those being moved forward in time then originally intended, and even then it's been more or less canonically confirmed that Ben was prematurely aged (partially due to Tattoine's brutal climate, and I'm sure the stresses and cares of life in hiding didn't help).