You can exclude your router from search by going to about:config and creating browser.fixup.domainsuffixwhitelist.<routername> (Boolean) with value true.

Disable all searching in the address bar by changing keyword.enabled to false.

This is not my problem, just an example.

I never want to search anything theat begins with protocol:// in the adressbar. I never want to search anything in the adressbar, because I have a search field.

Go to about:config and change keyword.enabled to false.

I did that before. It still wants to use search in most cases instead of following the URL.

I want the adressbar to not search. Never. It's an adress bar, not a search bar

I have never had any such problem. Have you switched off all search suggestions in Settings on the Search and Privacy & Security pages? If so, I suggest restarting in troubleshoot mode to see whether the problem still occurs.

https://support.mozilla.org/en-US/kb/diagnose-firefox-issues-using-troubleshoot-mode

in most cases

Does this only happen with single words? Try changing browser.fixup.dns_first_for_single_words to true in about:config.

It will still do a search if the query starts with "?", "@" or a search keyword.