People use it purely for that reason. If they don't, their usage will drop, which will reduce their revenue. The fact that this revenue comes from Google is largely a byproduct.
Its not a perfect system, but it should somewhat work.
I'm not sure - I guess the same motivation that supports the open source movement. I am satisfied that the actions Firefox has taken so far does tend to support my interests.
But many of us who used it from the start think it was a much better browser before. For a long so much was sacrificed for next to no improvement.
For me it was more or less rock solid at >800 tabs and with a lot less memory and more exciting extensions than I have now.
I admit this wasn't everyones experience, but as a superuser tool it has degraded a lot over the years.
That said it is still the best browser for me: I don't think anyone else except Orion (which is Mac only) has actual tree style tabs (not to be confused with vertical, non indented tabs as seen in Opera derivatives).
Firefox is my union representative. They are better able to fight for my interests against Google than should I go it alone and use Chrome.