Man 30 years older is showing interest... is he genuine?

How can I know how trustworthy he is? We don't meet very often, but I have noticed his attention towards me. Even though he's older, he's kind of a role model for many young girls and he probably knows that many crush on him as well. Maybe that made him very confident in approaching me in the beginning. He started off by just staring at me a lot, holding the door open, holding intense eye contact, being super charming and making fun of things I said.
He also waited for me until I came out of a room to wave at me and another time, he timed it so that when we saw each other, he had the whole hallway to walk down and he made a very manly stride out of it.
He regularly boasts about how great he is, comes a bit too close in my opinion, does me little favours and tells people how absolutely wonderful I am.

That was still not enough for me to think he's into me, but now this: he's trying to be receptive to what I say and do and clearly copies me in my interests. He just seems to give me more attention than the others, or at least make it seem that way. When other people are around, he manages to get my attention on him anyway and constantly wants that kind of validation. That I look up to him and all that. Once he asked me to play a particular song he heard me play on the guitar before, and he said "play it just for me, just for me". We were alone and his tone was rather seductive.
Other times he told me that I look nice, his body language is purposely laid back always, he has stared at my body parts, he seems very aware of me and that I could possibly look at him and he still gives me lingering looks when he enters or leaves the room. When he contacts me, he tended to become a bit annoyed because I took my time in replying.

I'm not really clear on how to handle this, as I need to know whether he's pursuing me for the right reasons (if he's pursuing me at all). It's a bit stressing to me and I really would like to have peace of mind...
Man 30 years older is showing interest... is he genuine?
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