In her first appearance in the X-Men, she clearly DOES know who Kurt is, and is the one to tell him to ask Margali about what really happened the night she took him in.
Yeah, and that scene was referenced in the issue where Mystique was unable to harm Kurt in the training sequence. So I dunno.
When they are no threat to you and you don't seem to care, yes, it pretty much does.
It's not like she kills random people for no reason or for fun.
How many decades of repeated, cold blooded, unrepentant murder would it take to convince YOU that someone had no intention of ever reforming, despite repeated offers?