1. Illyana is a mutant, uses magic, and sort of also classified as a demon. Molly's free to pick up on any of that.
2. Sure, emotions and change in emotions are free game. It may be harder than it would with a normal person though.
3. No. I'd be absolutely cool with Molly trying if it ever somehow came up but she probably wouldn't be able to, Illyana has super intense telepathic guards that even the most powerful telepaths can't get through in her world unless she lets them.
4. Yes! It would probably be the worst thing ever for Molly though.