Yes, they pass a fraction down to other companies that generate traffic for them, it's a little known model.

No, they don't. Firefox represents essentially $0 of revenue for Google because their market share is tiny and rate of adblock usage is high.

The only reason Google gives money to Mozilla is because they don't want to get sued for monopoly.

Source for this conjecture?

Firefox market share: 2.17%

Firefox ad block use: 17.81%

Remaining addressable Firefox market share: 1.78%

So essentially peanuts.

Especially since most of said users would have used Google anyway.

Seems to me that percentage is commensurate with the "peanuts" figure Google pay them, vs their annual revenue.