This is regarding the 4/4 version of Firefox. I'll get up to testing the more recent build shortly.
Firefox does not seem to start by itself. If I put firefox into Internet Application Integration so that I can launch web URL objects, or open a web page from Thunderbird, that does not work until I install Run!
The bitwise port starts without any help from Run!
Strange. I just used IAI to make Firefox (one I just built using the full path to it) the default web browser application and opening a web page from Thunderbird changed to Firefox from the previous SeaMonkey as expected.
Clicking on a web URL object such as blonde guy still opened SeaMonkey, opening the properties, showed under Browser, D:\Programs\seamonkey\seamonkey!lk.exe which is why it kept using SeaMonkey, without the --no-remote parameter, the browser, even the older SM, just opens a new window in the running browser. I assume if I did not have SM already running, it would have opened the older browser that the URL object points to.
Not the best way to set things up in my opinion and likely the reason that IAI doesn't seem to work for the system installed URL objects.
Thunderbird, I'm not sure about though there was an issue on the Arca issue tracker where some one had a similar problem with the Bitwise build of Firefox, he finally worked around the issue by setting up Thunderbird to use Firefox directly.
There's no code changes between the Bitwise build and the one you're using.