Safari changes original URL making it impossible to visit the site I want to visit

99% of the time, Safari does not change the URL. Safari connects to Site A and the site sends a redirect to Site B. In this case, Safari is reacting to whatever Site A is telling it.

The exception to this is if you have some kind of filter or malware installed that intercepts this request (this is common with search engine overrides where malware redirects search queries to a different search engine.

Without knowing the sites in question, it's impossible to tell whether your experience is expected or not.

There is something very wrong with visited sites. For while it worked as expected. Now, it keeps actual page from the site, that is not necessarily home page. For instance I get a single article form news site, over and over again, and I can’t drop it altogether form visited sites list. It comes back with the same page if I visit that news site next time. Or I get logout page from my bank.

it is insane.

And obviously it worked way back then, until Apple made “improvements”.