mysterious blue tit behaviour

I have asked this in the open forum but want to get an expert's opinion:

We have a blue tit building its nest at the moment and we observed some mysterious behaviour, which I don't know if it is courtship or defence. I hope someone may shed some light on this.

Yesterday evening (https://www.youtube.com/watch?v=JZnXn-BbaIo), the nesting blue tit entered the box. A while later another one came with its wings lowered and seemed to be "begging" outside the box. Inside the box (https://www.youtube.com/watch?v=bKVmYTpa5OI), the nesting one "bit into the air" even if it didn't see the other one later. It didn't look aggressive as it didn't spread its tail or made any noise. I am not sure if the one side was the male as it looks different from the male that used to come.

A while later (https://www.youtube.com/watch?v=IMJz3tjQgY8), the blue tit outside was still lowering its wings and seemed to be begging outside the nest box. You can see the nesting one's behaviour (https://www.youtube.com/watch?v=JAgXx-VgWKw).

This evening, we saw the nesting blue tit "attacking" the one outside (https://www.youtube.com/watch?v=zuhbhWbahp0). Is this really an attack?