Can she read your character's mind?: yes but he's going to know what that feels like thanks to living in a house of psychics.
Can she dig deeper in your character's mind?: yes! he's thinking about food, sex or murder most of the time sorry :( he's purely ego-driven so she'll find a lack of impulse control. also he's killed soooo many people and monsters. like so many. his power (draining life from others by necrotizing their flesh) is so gross!
What does your character's mind look like?: think of the worst static in the world and compress it into liminal space. never feeling like there's enough air, but breathing fine. sometimes there's blood on the walls of a long hallway or an endless room, other times it's empty with a singular chair. he's spent a lot of time in and out of psychiatric hospitals and it'll smell like disinfectant or bleach. he's jokingly referred to as having "swiss cheese brain" because he's so unpredictable and compulsively lies, so his mind will reflect that.
Can she dreamwalk in your character's dreams?: she's welcome to dreamwalk! but he barely dreams, and if he does there's a lot of mixtures of sex, gore, and homicide, or all three at once. sometimes it's of his time in russia and his handler, except the face of his handler is blurry.