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Firefox could be doomed without Google search deal, says executive
(www.theverge.com)
A place to discuss the news and latest developments on the open-source browser Firefox
The answer to the second question is the answer to the first - there have been a ton of attempts at alternative sources of funding, but it's hard to come close to the ~half a billion USD the default search deal provides. So far the branded services you're calling for don't seem to have been able to pull it off, and I haven't seen any signs that donations would be able to either.
(Although as for email with Thunderbird...)