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.
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.