In some cases it really matters who is initiating the conversation and I think that way you do get some of the information of their origin story. I personally choose who I think is suited best to lead in the situation, sometimes even when I lead with a companion, the game still initiates with my custom character, I then have to unlink the group and try again.

I have no idea how the game decides or behaves in coop.

I'd assume for the best origin story experience and ending, you should go for the origin character as your "main" character. But I haven't finished the game myself yet.

As far as I remember the Switch doesn't actually use uPnP. The only thing that I had to do to achieve NAT Type B was an outgoing NAT with static port enabled. If I understood right, NAT Type A can only be achieved if your device literally had a WAN address.