If you are using any non-Apple "anti-virus", "cleaning", or "Internet security" junk, anything at all in that broad category of useless garbage, don't. A lot of things won't work if you do. It's not sufficient to merely "deactivate" such things. They must be uninstalled according to their instructions. Rule 1 of Macs is don't install junk.
The macOS firewall is unrelated to an inability to load web pages. To learn about the application firewall read Use a firewall to prevent unwanted connections on Mac.
As such I assume that something goes wrong with my house broadband.
That is certainly possible.
Please review the following Apple Support documents. Some of the information will be redundant but review everything to determine if there is something you may have overlooked.
If you don't get anywhere, you can use the following procedure to determine if the problem is internal or external to your Mac. Causes may involve your router, your ISP, the DNS Server(s) it uses, or certain user-configurable options.
- Shut down your Mac.
- Load macOS Recovery by holding ⌘ and r (two fingers) while you start your Mac with a third finger.
- At the macOS Utilities screen, release those two fingers.
- Choose Get Help Online.
- Safari will launch, but it will lack your bookmarks, favorites, history and other preferences.
Determine if the problem persists while using Safari in that mode. After that, restart your Mac normally, and reply with your observations.