Was I misreading the vibes he gave off?

Hi guys!
I need some preferably male perspective on this, and if possible, some good advice. This is about a quite older man with whom I happen to be pretty good friends because we are in the same professional field. In the beginning, I immediately noticed that he was very attentive towards me and did all the gentleman things like opening the door for me, doing random favours and such. He also bragged a little, stared at me and blushed, but I brushed it off as a charming, old school guy who finds a young woman attractive.

Now, I don't really understand if he's up to something. More things have happened. For example, he clearly wants me to rely on him and catch my attention, he tries to be extra cool in front of me, stares at me still, tries to find common interests, sometimes has a very soft look in his eyes. When I was in trouble, he was being very empathetic and communicating a lot of that in the way he looked me in the eye. It was very expressive.
He also touches me in an officially friendly way, but I'm never quite sure if he thinks something more of it when he lets his hand linger for quite a long time. The touch barrier is pretty much down, but that could just be the way he is.
When others are around, he does tend to stare at me, but not make it obvious. Also, he seems sad when I leave.

He told me I'm good looking and seems genuinely interested in my work. When we were supposed to be in contact for work, he seemed pissed that I wasn't replying as fast as he might have wanted me to. That was not unprofessional, I just didn't see the necessity to contact him more often.
He mentioned having two kids, so that cleared up right away, but never a woman. Then, he mentioned his wife in front of others, and for some reason, that perplexed me. Was I a fool to have noticed his behaviour towards me before? Is he "just" an alpha male who is like this with all women?

I can still emotionally back down, but am I misreading/overanalyzing?
Was I misreading the vibes he gave off?
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