How do I know whether SQL Server is in per-seat or per-server mode? How can I change it? How can I add licenses?

A. The answer to all these questions is the same :-

Click Start
Click Settings
Click Control Panel
Double-click on the licensing manager applet here

All the info and changes are here.

For details on MS's licensing, see :-
http://www.microsoft.com/SQL/productinfo/licensesummary.htm
http://www.microsoft.com/SQL/productinfo/pricing.htm