> When you start Firefox two times in a row, the dialog "Firefox is already running, please close the running instance" or something like this pops up.

This is actually due to shutdown (rather than startup) being too slow. Your profile is still in use from the instance of Firefox taking too long to shut down, so when you start a new instance it hits this error. This should be a little better with multiprocess, because web pages are run in a separate process, and we kill that process more quickly, so shutdown should be faster.