I've got an error "This site is blocked due to content filtering."
DNS stands for Domain Name System. It takes your human-readable URL (e.g. google.com) and converts it to a numerical IP address for your computer to read (e.g. 172.217.11.14). 

It looks like the DNS settings on your router are pointing to OpenDNS servers. OpenDNS is a free content-filtering service that prevents access to adult/malicious sites and is not a spying/sniffing tool (in reference to your second question). Basically, when your computer tells OpenDNS "Hey, look up this website for me," OpenDNS compares the website against a list of adult/malicious sites and if it is on the list, it tells your computer "no, you can't access that website."

To no longer use OpenDNS:

If you have access to your router's configuration page, you can change the DNS settings to point to other DNS servers (e.g. 8.8.8.8 and 8.8.4.4 are Google's free DNS servers you can use.) 

If you don't have access to your router's configuration page, and as long as there are no rules on the router to prevent it, you should be able to enter a different DNS server address in your Mac DNS settings (which you have pulled up in your last screenshot). Click on the "+" button and put in the two Google DNS servers mentioned above.