Is married dude coming on to me? Does it mean anything?

I want to put an end to my confusion. It seems like we are friends and I want to be friendly with him, as would be normal. He's kind of my superior, his job is to help guide my studies, but it has a friend-aura.
Not knowing if I'm right with my feeling stresses me out a little and I can't act as natural with him as I would like. I feel paranoid, yet also like it's reasonable to wonder about it.
Is he crossing boundaries or conveying something?

He's having a dreamy eyed look when looking at me and in general, he's reacting sensitively towards me. He touches my things as if it's normal and without asking, and he wants to share his things with me too. He makes that very clear and says things like "you can use this, this is basically yours now". Seems very intent in that. When at a distance, he tends to stare at me, sometimes while smiling and holding eye contact. The staring is there when we're one on one too.
There's nervous body language, running his hands through his hair. He's empathetic towards me and caring, yet I think he expressed feeling jealous over one of the guys who hit on me a little in front of him.
He said I look good, that he likes me. When I don't give him enough attention, it seems he takes that personally and can become quite childish and almost mean. In the beginning, there were blatant flirtatious stares while smiling in my direction, but I deflected that. Now, it's more like stealing glances. Oh and the biggest thing: a few times when he showed me something on the paper, he positioned himself really close to me and let his hand linger next to mine quite long.

Is it all in my head? Does it have to mean anything?
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To user "asshole" who apparently blocked me: I just don't understand why such a discussion should be reason enough to block someone. I disagree, I think men and women can be friends, simply because they know where to put their attraction to one another. If one does not do that, that puts the whole relationship into a weird context and that should, frankly, not be happening in certain situations.
Is married dude coming on to me? Does it mean anything?
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