Firefox isn't doomed. Not only is it still a good web browser that many (myself included) continue to use daily, inertia will keep it installed on millions of PCs. As far as I know, Mozilla and Google maintain good relations. Even if the deal that provides money from Google to Mozilla isn't renewed, I doubt they will entirely disentangle themselves from each other.
Firefox is doomed because its lost its developer foot hold, anecdotally most devs I know refer to it as a joke and use Chrome instead. Its a browser that relies on recommendation to exist, and it no longer is getting recommendation. On a technical note each version isn't really getting any better, historical problems have never been addressed, version fragmentation is occurring, on several matters its in direct confl…
What exactly do you mean by that? The UI in a browser shouldn't do anything but get out of the way and display the web page's UI.
Personally, I don't even want to see a menu bar unless I hit the ALT key - which is working nicely for me in Firefox right now.
And I don't notice any "laggy behaviour". Although I haven't run any comparison tests so maybe I'm missing out.