GDPR changes. Now you have to give specific consent for processing - see
here.
Now you must accept the agreement because without cookies then parts of the site just would not work.
Yes till I close it.
By that do you mean you clear cookies when you close your browser. If so then thats the reason why - the only way that the site can know if you will accept cookies is by setting another cookie to say you've accepted. When you clear cookies then I've no way of knowing that you've previously given cookie consent, so the message will re-appear. Same with login which also uses cookies.
Have you not noticed that within the past week just about every website now presents you with a cookie notification. I sure have. Every time I go to a new site up pops their cookie consent and/or privacy policy. I'm getting a bit bored of it now.. but that's legislation for you
Not all cookies are bad.