Is this man trying to hit on me?

Is he trying to make something happen?

I noticed that he's been staring at me a lot and he also gets either weirdly calm and quiet in my presence and makes me wonder what he's thinking, or he is super cute and smiley. He also seems very attentive to how I feel, what I say and what I do, he kind of imitates my gestures and the things I say and I think he also checks out my social media a lot. When he's around me, he's started to touch me when it's appropriate in appropriate places, but he does it for very long. Like that, he really closes in on the personal distance. He also opens the door for me, lets me go through the door first and so on. When he lifts something and I want to help, he doesn't let me. Also, he's teasing me a little, but it's not really mean.
Sometimes he looks at me with a very tender look in his eyes and smiles a little. Also, he's staring at me from afar and making sure I notice and look back. He simply holds eye contact until I notice him... !

He seems quite confident, I hope he's not too used to getting girls. I figure that time will tell his deeper intentions.
Is this man trying to hit on me?
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