The "first part" just explains that you can configure static DNS servers at both the host and the router level.
The router does have a firewall. It is a kind of primitive one though. It only blocks all inbound traffic (except ICMP Ping Echo) by default. Enterprise-grade security routers support more firewall features. This being said, I doubt the firewall at the router is causing the issue. You mentioned that you do have anti-malware software running on your device. I am wondering whether the anti-malware is blocking your connection. Can you disable the anti-malware temporarily and test those websites again?