That seems ... well like quite a leap. She doesn't look like her and Sasaki could know her from the time he spend under working Arima. (Or from some immediate post-lobotomy events.) The Koo part probably refers to the name of her superior Koori Ui not to Kurona.
That's the guy from Tokyo Ghoul: Jack. Unlikely to be scheming something going by that story.
Yeah, I guess it was. She just seemed too weird!
Definitely didn't recognize Fura. There's way too many regular businessman-looking investigators in the CCG. That explains why he's so familiar with her I suppose.