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The green cables I usually see are grounds for the ONT. Here, it looks like its spliced into that power adapter, so maybe power for your ONT or something? In either case, doesn’t seem right, lol.
Probably a bad cable somewhere as long as the router, switch, and device are all Gigabit plug ports.
It’s possible as long as the wire in the wall goes to where you need it to go. It can’t be through a switch, so both ends need to be the same cable. Just search HDMI over Ethernet on Amazon. Both ends need power as well.
Wifi Analyzer
Stick something in the top holes and pry out I’d imagine.
Running Ethernet is always the only answer.
You can’t adapt it, but you can check the back side of the outlet. If it uses a Cat5e or better cable, and there are no daisy chained wired to it, you may be able to. Once you confirm that, you’ll of course need to find where the other end goes to as that would have to go to your router/switch.
Your router routes. It also assigns IP addresses to devices. So no, you can’t just connect a switch to a modem and be Online. It may be possible if your ISP gave you multiple IP addresses and you set them static to your devices, but you also do not want your private devices directly on public Internet.
Bad cable somewhere.