How Asuka could know the reason of why he was attempting to murder her?
Apparently being part of a primordial ur-being gives you unwanted, unpleasant insight into others' and yourself. It's perfectly possible that she didn't understand the exact why, just the general why (the strangling being a gesture more of hurt than malice).
Why her eyes looked so "empty"?
LCL IS A HELLUVA DRUG!
Jest aside. Post-trauma shock. Instrumentality was a lot to take in. Shinji's got the same thousand-yard stare going on, though I tend to think his is because he's been waiting around weeks or months for people to come back, slowly losing his goddamn mind.
Unelaborated-upon. One imagines she projected them onto herself when she reformed (apparently the last moments with the MP Evas left an impression on her psyche). If they're covering any real injuries? Who knows. But you wouldn't be using a bisected arm to perform a caress like that, so I'd lean towards "no." Shinji similarly appears to have envisioned himself as clothed.