The same goes for ad networks. YOU are responsible for making sure the ad network is compliant. If you include a non-GDPR complaint ad network script on your site and somebody complaints, then you are in for it because you were ultimately responsible for that network being able to track the user on YOUR webpage.
If Facebook is GDPR compliant and has consent from the user then you are in the clear. If Facebook is not GDPR compliant and tracking people who aren't users then a EU or local court will set up a campfire under their asses (German courts already have).
IP addresses are definitely personal data (PII and Personal Data are different, the GDPR defines and cares only about the later, PII is mostly an US term used interchangeably with PD on the internet) German and EU courts have ruled that since an IP can be traced back to a person, it's personal data. Unless you have a good reason to log it (hint: firewall and webserver logs) then you need consent for it.
It realy is very much like environmental regulation. Before things like the EPA etc. came to be, it was a toxic 'everything goes' type of environment. Transition to a regime where businesses are held to data responsibility might be painful at first, but ultimately hugely beneficial to all.
They acquired your name, birthdate, address, etc. And they didn't aquire it through your website.
Calling IP address or screen size "person" identifying information seems a stretch to me.