In addition to what others have posted, as long as you’re honest about it just being a hat and not making any special claims about it (like it was owned or worn by a famous person), I think you’re good.
Nah, where I work (and where we all work, teally) we have legitimate confidential information about our customers... that the appropriate employees can access appropriately. That's not an abnormal use case.
Definitely has something to hide, especially if he's formatting his computer every time he has a "problem". Not that data can't be recovered after a format anyway.