Q: When you interact with other people, do you view it as interacting with an aspect of yourself? Do you feel like I am you, in another Point of view, no matter who?
A: That is a good way of putting it. There are several "points of view" that are all true simultaneously:
I am me.
I am you.
I am everything.
I am nothing.
Since what I am and what you are is everywhere and every-when, then it can also experience itself as any part or all parts. It is similar to how on a cloudy day, it is dark in my closet, grey outside my house, the sky is blue above the clouds, and out in space the "sky" is black. All these different perspectives exist simultaneously and the experience depends on where you are experiencing from.
So in answer to your question, sometimes I view it as interacting with another person, sometimes as interacting with myself, sometimes as interacting with infinite being and sometimes there is no one at all interacting.