Do you ever visit the two of them, or is just him alone?

If I recall correctly, those actions are called mirroring, or something similar. They can indicate a level empathy. They can be intentional or involuntary. It's meant to make you feel more at ease.

Yeah don’t be alone with this guy. Kind of giving off Single White Female vibes.

Seems like he likes you

Especially with the mirroring part

Curious, why are you going to visit him?

He does sound weird. 😳