Add a second PC (server) - How To?

FYI, You should not post your public IP address.

The Synology person sounds confused. Plex works on DSM 7.0.x and DSM 7.1. There were problems with DSM 7.1 beta. See this post.

Not sure what that means.

Are all three servers listed in Authorized Devices? If not, which ones are not listed?

Can you access the Plex Media Server via its IP address: http://192.168.1.181:32400/web?

Can you access the Plex settings via https://app.plex.tv/desktop/#!/settings/web/general? You should be able to access the settings for all three Plex Media Servers. You posted a pic above showing DS720 and OldPC. You should now see NewPC added to the list.