Though I understand where your coming from in my view though I think childhood is an important element to Asuka's characters regardless of universe. Like I wanted to know what the difference was between the doll in the manga and series and the puppet in rebuild which she talks to. Also is she as neglected as the original Asuka's in terms of childhood or did some one betray her hence why she has serious trust issues. There little things I know but in the original series these small things really carried the characters even in miner flash backs.
Also added note I want to see her left eye under that patch...
Personally I'd like to see Asuka's past told to Shinji by Mari at some point in the movie, I think it has potential as a scene in the movie. Maybe Asuka is in a desperate fight and Shinji could do something about it but he feel useless or similar. I'm not a huge fan of large flashbacks at the end of the story so I hope Anno avoids them.
Regarding Asuka's angelic eye not only I want to see what is like but I also hope it becomes a crucial parts for Gendo's plan. As far as I know it's one of the last angelic active thing left to use.
Yeah I get that Q isn't meant to have all of the foma Rei's memories but in 3.33 its hinting that she is starting to remember as in the tank scene when she recharging if you look closely the other Rei appears to her dressed in school clothes then vanishes in a blast of bubbles. Its a real blink and you'll miss it moment and its only after Kaworu takes the Walkman away to fix it for Shinji which hints that she may have been hiding in there. Its just my theory but I think in the tank scene the two Rei's have merged hence why Rei Q starts reacting and having emotion.
I think that phantom Rei was just the reminder in the classic "setup, reminder, payoff" scheme.
We already had the set up at the very beginning of 1.0 when Shinji saw a Rei in the middle of the street, then we had a reminder in that scene with Rei Q in 3.0 and we are probably gonna get a payoff in Final. I doubt it's going to be a payoff in the classic sense but I'm sure there will be another mysterious Rei appearance.