No, it is not polite. you use words like 'bloody, flipping, damn' when you are angry. Mostly anger and politeness do not go together

It is definitely not formal. But it's not impolite always. It depends who you are talking to.. If you are with people close to you and you say "that's bloody brilliant" it would be considered a compliment.. But if you are not with people close to you it's better not to use it.. as it can be misunderstood.

If you say it in the United States, the main thing that we think is that it sounds British. But yeah, I think it's not very polite.

Not really, but it is very common in informal conversations--especially in British English. Here in North America, we rarely say "bloody" unless we're literally talking about blood.

This word is also regional. No Americans use "bloody", unless they are talking about a medical problem.