Apple - 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. 126.96.36.199).
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. 188.8.131.52 and 184.108.40.206 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.
Your assumption that the mac is blocking this could be incorrect. It also could be a VPN software like Cisco AnyConnect which uses OpenDNS servers to ignore the local DNS servers and settings.
By the screen shot, Your mac is trusting the router 192.168.1.1 to filter all your traffic, and that router is the item that’s configured to filter some sites.
If you can’t find some network software that installs a kernel extension or uses VPN hooks / network filtering in Catalina, the next step is to look at the group that runs your network setup? You will need to discuss with them how they’re configured the filters that direct traffic.
Lucky for you, they left a calling cart there in the block page - [email protected]
Perhaps they have a log in process to ensure you’re not a minor. Think of this like mailing a package. If your mail service goes through a company that checks each address and blocks delivery to some, you would need to either get them to change their rules for your packages or choose another company.
In net-neutrality terms - you need a VPN or different agreement or a different DNS provider.
If this filtering is likely legally mandated in your country, check with your lawyer before you try to get around a content filter block for minors. We are not lawyers and can’t be your lawyer, but this is a very topical subject about freedom, censorship and the internet. Good on you for learning about how your privacy works. If you’re not a minor - vote for net neutrality and better transparency from your IT setup team. If you are a minor, get ready to vote and this is what algorithms and surveillance looks like in the 21st century.