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Yes, and some Bayesians would even distinguish between e.g. 50% certainty in the coin landing heads on the next toss after 50 heads and 50 tails from your rational beliefs before testing the coin at all.

You can use the beta distribution to calculate the probability that the actual probability is between 45% and 55% given 50H/50T, and it's around 70%: graph. So in that case I would say I believe the coin is fair with 70% certainty. With 0H/0T it's around 10%.

The more tosses the more likely the actual probability is between a certain range, so the more "precise" it should be.

https://plato.stanford.edu/entries/imprecise-probabilities/

Articles from Stanford Encyclopedia of Philosophy are very interesting, but way too complicated for me. This article is no exception, very interesting, but my point is much more general.

By using probability I'm not trying to find an accurate value of belief, what I'm trying to do is show is that even in simple questions people have an unwarranted level of certainty, even people who call themselves "skeptics".

Sorry, wasn't meant as a critique: just something else that is interesting to think about.

Yes. I didn't consider it a critique. I think we are talking about the same thing except at different levels, like those Wired videos of explaining one concept "in 5 levels of difficulty".