They like water. I had one that sat in the shower after I got out. Someone suggested the warm steamy air is good for their fur.

Cat's concept of personal space and boundaries is quite different from ours, it seems xD

I had two kittens for awhile, they are relentlessly clingy.

No they are just friendly

Not all cats, no.
If they were born and raised in an environment where humans treated them well, yes.
Don't worry about it; he just likes company and finds your activities fascinating - like TV for cats.
If it does bother you, he'd be happiest with someone who can love him in return.