Why a belief with degree 1 is not affected by new information which is counter-evidence to that belief?

That's how degree 1 is defined: such strong a belief that no evidence can persuade one to abandon it. (You shoudn't have such beliefs, needless to say.)

The difference between what you call traditional epistemology and Bayesianism involves lots of things. I think one of them is their objectives - the traditional epistemologist and the Bayesian in general have different goals. The first one is interested in posing the correct norms of reasoning and other sources of beliefs (perception, memory, etc). The second one maybe is more interested in modelling rational structures for a variety of purposes.

I don't see the difference. Bayesian epistemology is a set of prescriptive norms of reasoning.

That being the case, the puzzles I brought maybe are not of interest for Bayesians - but that does not mean Bayesianism solve the question of what is the correct thing to do in such cases.

Bayesianism explains the problem away - the problem is there only if you use notions like defeat or knowledge and insist that to build your epistemology on them. Your puzzle shows that it is impossible. The fact that Bayesianism is free of Gettier problems is an argument for Bayesianism and against "traditional epistemology".

To make an imprecise analogy, ancient mathematicians have long wondered what the infinite sum 1-1+1-1+1-1... is equal to. When calculus was invented, people saw that this was just a confused question. Some puzzles are best answered by rejecting the puzzle altogether.