I just inferred she hadn't ate much that day considering how weak she was. Even on an empty stomach, people still vomit (happens to me at least on the few occasions I skip dinner and wake up the next morning feeling really weak and prone to vomit). However, I will concede to this nitpick, as the end result in your story ended up with Asuka agreeing to have food with Hikari.
With the second, I don't think Shinji's ever talked with Misato about why she joined Nerv (beyond the obvious "fighting Angels"). He knew she had issues with her father, but not how it motivated her.
I can confirm this isn't the case. Episode 12 is the episode where Misato gave Shinji full detail about her father.
Here's the dialogue:
"Shinji, yesterday you asked me why I joined NERV. My father was a man who lived for his research, for his dreams, to the exclusion of all else. I could never forgive him for that. In fact, I even hated him.
[Shinji's thought: "Just like my father."]
He never took care of me, my mother or the family. His friends always said he was very sensitive and delicate. But the truth was the he was just a weak person who didn't want to face reality, the reality called his family. He was like a kid. So I agreed with my mother when she decided to divorce him because she was always crying. He was depressed about it, but I laughed at him because he deserved what he got. But he sacrificed himself to save my life during Second Impact. Then, I didn't know whether I hated him or loved him. The only thing that was clear to me was I wanted to destroy the Angels who caused the Second Impact. So, in order to do that, I joined NERV. It might be that I still hate him, and just want to avenge my father, so that I can free myself."
So she basically spelled out everything to Shinji as they were over looking the city of Tokyo III.
With the last, the Fuyutsuki scenes will delve into this in detail.
Sweeet! Look forward to it