Answering myself. The router is inoperable as it cannot be used. Switched back to my old router.

During installation, I used the Quick Setup Wizard and then changed a few settings under the advanced tab. Have not used Smart Connect, but I have set each 2.4 and 5 GHz band separately. Have then changed the WAN side (Internet) DNS addresses with either Cloudflare's or Google's free DNS addresses. Haven't used my ISP DNS, which by the way don't seem to be correct when the router should detect them, don't think my ISP has 1.1.1.1 and 10.10.10.10 as DNS, anyway they haven't before, 1.1.1.1 is Cloudflare, right? Since then I haven't changed almost anything. Have added the above DNS addresses also under the LAN side (DHCP server) but that doesn't make it any better either with or without.

Have tried with changing the MTU size to a lower size, 576, 1400 or 1460 but no solution. Tried turning off the router's firewall and also my computer's (using Ubuntu) but nothing better. I've even cloned the MAC address. Is there something in the router that restricts web pages? There are functions in HomeShield that do that. Eg Network Security. I have not set any such or subscribed to any such feature. Is there any feature in the free HomeShield that restricts and blocks web pages? If so, how do I disable it?

My computer is connected with a cable to the router. But the router behaves the same with the devices that are connected via WiFi. Because of that, none of these devices (eg Google Home, Google Nest or smart TV) work satisfactorily.

So the router is not usable. It may not have been very expensive, but a new router is still expected to work. And that with simple settings, doesn't have the time required to sit and try different settings back and forth. When I bought my latest router, before this one, it worked out of the box, right away. Quite disappointed with TP-link now.

@Liverpool20 

Thanks for the reply.

None of the clients are able to connect to these sites. Connections to other sites are also not good. I have reset the router several times, to no avail. At each reconfiguration I have only set my wifi settings (LAN), possibly DNS settings (Google DNS, Cloudflare) but of course I have also tried using ISP DNS, nothing works, can't reach the websites. Like I said, most sites on the internet work less good but they are reachable. Sites I know can't be reached are pCloud, Proton VPN, Proton sites, my bank (lives in Sweden) and possibly many other.

My ISP provides me with a Technicolor cable TV modem. My old Netgear router works perfectly with this modem, never had a problem with internet. I have now connected the TP-Link router as an AP after the Netgear router, letting this router connect to the internet (disconnected the Netgear router's wifi), and then I can use the TP-Link router's wifi functions. But I can't connect it directly to the internet. I'm starting to think it's an ISP issue. When I connect the router with the default settings and then activate a VPN, all of a sudden I can reach all pages, but if I disconnect the VPN, it doesn't work. It indicates that my ISP is somehow not working optimally. Or maybe that their modem isn't compatible with the TP router.

I think it's far-fetched though but I don't know. It's very confusing though.