I HAVE BAD NEWS FOR YOU FINGOLFIN
Unfortunately for you, your team actually had picked an alternate player previously! So you are back on the unassigned list!
GOOD NEWS is, you get to try a new team on for size!
As for your questions:
1. from my understanding each team is randomly assigned to the axis or the allies
Yes that is correct, UNLESS teams agree before hand, who will play which side play.
2. is each player also randomly assigned to their country/countries, or do they choose by themselves, or how does that work?
Each team will decide who will play what powers, over their games. That is entirely out of the hands of chance!