Can Thomas talk/send images/send notions into your character's mind? Yes.
Can Thomas poke around in your character's head? Yes.
To what extent is it cool for Thomas to explore you dude's brainpan? Everything is cool, but if you could ask me before sharing details about Jesse's meth business with any other characters, I'd appreciate it. It's something that affects a lot of other characters so I'd like some prior plotting over how that's revealed to the general public and the consequences of that to Thomas himself.
What kind of stuff would be cool to Thomas to dig up, if he spends more time snooping in your character's head? Jesse has some dark shit going on in there. He's not who he appears to be, in that he's a drug lord/murderer working as a school nurse. But he also very much is who he appears to be, as someone genuinely protective of children and young people and innocents. So, yeah, he's violent and psychotic, but he also wants to be everyone's kindhearted big brother.
What stuff do you NOT want Thomas digging up in your character's head? If it's too messy for Thomas to catch onto the details of Jesse's drug business then it's something you could reasonably ignore, because Jesse tries not to think about it when he's not actively engaged in it.
Do you want to do any kind of bleed over stuff while Thomas still sucks at using this power? Sounds cool!
Contact? pana