Don't know how the Mac works, but on a PC you can go to Control Panel & there's a Add/Remove Programs function. Also, some programs have their own uninstall applet built in. You can right-click the program group and see what's there, or go direct to the program folder to see if the uninstall applet is there.
As far as getting the new Firefox w/o the old, you can either get it through another browser, or else download the install package thru Firefox, uninstall the existing version, and then run the install package for the new version. At some point, we all, hypothetically, had to get Firefox w/o already having it, right?
Either way, uninstall the old version before installing the new. Uninstalling should get rid of everything, not just the main program files,
Other can speak more succinctly and/or in more precise detail about this, I'm sure.