So really I have 3 questions, but they are all pretty straightforward (for once):
Can an add-on in Firefox see if there are multiple instances of Firefox/the firefox process running?
Since the only way (in Windows, at least) to have multiple instances of Firefox running is by having them run under different profiles, is it possible for an add-on to determine which profiles the other instances are running under?
Could an add-on interact with the other process? Specifically, could it do things like close the other process or tell it to open a new window with a URL specified within the add-on's process?