There does seem to be something going on there, but it's still difficult to say what it is. I'd be interested to see if you can narrow it down. To answer your original question, Unifi access points come with a PoE adapter for power in case you don't have a PoE switch, but other than that you can just plug the Ethernet cable into your existing network. You'll need the Unifi controller software from the UBNT website to configure the AP, and you should be connected to your LAN via Ethernet at that time. The setup is fairly easy.

The ER-X user interface is a bit different from a normal home wireless router, so it might look strange, but there are videos on YouTube to walk you through setup. I don't think you really need the ER-X, but it's not all that expensive, so whatever.