Products such as Cisco Umbrella cover both. There’s a DNS appliance inside the network, as well as a client software that installs on devices that forces them to use Umbrella’s public DNS server when being used on another network.
This means we can track everything on the company owner device, even when you are at Starbucks or at home.
Never expect privacy on any device and/or network you don’t have ownership and control over.
The security on your device doesn’t matter at all.
For ANY device to reach ANYTHING on the Internet it has to send a lookup request to a DNS server to get the IP of the server.
A privately controlled network can easily force all of those requests through their own private DNS server which captures all activity.
Use Firefox to browse it. This addon keeps FB in its own container so it can’t read anything from other sites you visit. https://addons.mozilla.org/en-US/firefox/addon/facebook-container/
Then just make a throw away email and use that to make a FB account.