Thor
Is it cool for River to read your character's mind?: Sure!
Is it cool for her to talk about it?: If she likes!
What might she find there?: He's a god, and his headspace is made of Incorruptible Pure Pureness (http://tvtropes.org/pmwiki/pmwiki.php/Main/IncorruptiblePurePureness).
Would your character notice?: Yes! Thor won't be terribly thrilled about it, but will mellow when he realizes River probably doesn't mean any harm.

Ricochet
Is it cool for River to read your character's mind?: Yes!
Is it cool for her to talk about it?: So long as she doesn't mention his secret identity.
What might she find there?: Self-confidence issues and guilt underneath a metric ton of wisecracks.
Would your character notice?: His Danger Sense would conceivably ping, so yes.

Mullin
Is it cool for River to read your character's mind?: Yes!
Is it cool for her to talk about it?: Yes!
What might she find there?: Mild combat-related trauma and a lot of uncertainty and loneliness.
Would your character notice?: Nope! Mullin's as psychic as a brick.