Is my boss being friendly or flirty? help?

salonity12345
I joined a new job last week. My boss is around 34, married, very extroverted and very friendly hence the reason for my confusion.
Our video calls together always overrun (even our interview did), he smiles at me randomly, and i feel him staring at me over video. If we have covered everything we need to within the slot and he can't 'delay' as he has another meeting he tends to apologise 'for not being able to talk more', or suggests the next call should be 45 mins-1 hr rather than our 30 mins.
In person, he stands very close, maintains eye contact and mirrors my body language/actions. When we had team drinks one evening, he teased me in front of others and playfully nudged me while doing so (first time we broke touch barrier), and when i did it back he looked at me for a bit as if he liked it. From then, everytime we stood and socialised with others, our arms would keep touching or he would accidentally' hit my arm with his elbow. When a colleague he's close to was talking asked me if i had a boyfriend, he diverted me from answering and asked if i would like him to take my handbag and coat (which i was holding) and keep it with him.
At the end of the night, when it was just me, him and another left, he held my handbag, stood behind me and helped me into my coat like a gentleman. When i told a colleague my boss took me out for lunch on my first day, he (boss) joked: i didn't 'take you out' for lunch, i wanted to go to lunch and you came... but i do need to 'take you out' to lunch! and he proceeded to make a plan to take me out to a japanese restaurant (he knows is my fav as he asked me my fav cuisine earlier) specifically next Friday (a day where people usually aren't in the office).
He also remembers every single detail i tell him. Yesterday when i dialled into our video chat the first thing he noticed and exclaimed was 'glasses!" (i hadn't worn glasses before in front of him).
I won't pursue for obvious reasons but would be nice to have an idea.
Is my boss being friendly or flirty? help?
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