To run a new, separated Firefox with a (possibly) different profile
firefox -no-remote -ProfileManager
It's always handy to have a "vanilla" profile, to compare how much the extensions tuned down the browser or try to understand if the error that you're seeing is caused by an extension. Having a "privacy" profile with some ad-hoc extensions helps too.
Mind you, -ProfileManager actually opens to the full profile manager interface (where you select a profile to run, or create a new one, or whatever). You can load a specific profile (that already exists) directly by replacing "-ProfileManager" with "-P [profile name]". (Omitting the name will open the manager, too.)
Thanks. Sorry I mis-remembered the flag(s) from memory. And be sure you're using both, to make sure the separate profiles do not share the same process or something like that (again, from memory; Google can quickly turn up the details).
Your memory is right. Without -no-remote you would end up spawning another windows from the currently running firefox. Without -ProfileManager you can't choose a different profile.
It's also a good idea to use different themes per profile (and I see you suggested it too).