Can she read your character's mind?: yes, it might be a little fuzzy because caroline's vampire powers are fairly strong but very untrained but parisa can get past that for sure
Can she dig deeper in your character's mind?: absolutely! nothing is off limits up to her canon point
What does your character's mind look like?: much like the woods in mystic falls, some spots are nice (a warm clearing, the pond/creek, a heathery meadow) and others are less nice (the tomb, the well, the lockwood cellar, her dad's torture chamber)
Can she dreamwalk in your character's dreams?: she has a recurring dream about the members of one direction falling in love with her, you're welcome parisa, she also has incredibly vivid dreams about being a barbara walters-esque new anchor/interviewer and interviewing various and sundry famous people; torture is also a theme that comes up in her more nightmarish dreams and a recurring nightmare of losing her dad because she becomes a monster and kills him herself