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You don't want another router, you want an access point. If the Ethernet run goes to a wall plate, look at TPLink Omada EAP615-Wall. You can connect the one run to that unit, which will give you an access point/Wifi in your room, and it still has 3 Ethernet ports so you can connect your PC, a switch, anything else to. You can use the same SSID, password, and encryption on it as your main Wifi router. The handoff between the units may not work as well as a proper full network buildout with a controller though, but it's a good option and relatively cheap.

Your other option would be to get a mesh Wifi system and use that cable between the main mesh router where you have it, and wire the second unit in the office. Mesh units also typically have a few Ethernet ports so you can direct connect your PC. More expensive option, but will manages roaming for your devices much better than just same named SSIDs.

Avoid powerline at all costs.

You can use a Cat6 punch down junction box if you have to and can't run a new wire, but you are adding a point of failure. It should still work anyway, just keep the twists as tight as possible to the punch downs and mind the total distance of the Cat6 run from point to point. Another option is terminate it, plug it into a mini switch, and continue on from there to extend the distance and keep signal integrity.

Normally I'd say uninstall the NIC from Device Manager and reboot, but it looks like it didn't work with a USB NIC either. When you tested other PC's, you had them connected to the same exact cable and port as the PC with the issue?

If so, you have something weird going on I've never heard of. Reinstall Windows and hope for the best.

Yes. As long as it's ISP > ONT/Modem > Router > Switch, you can plug whatever you want into the switch after the router.

If you need to finance a router, you probably shouldn't buy a router.

You don't need to run a wire if the satellite unit has good signal strength to the router unit, but wiring it will give you the best performance at the second unit in both speeds and reliability. You definitely don't want two routers, unless one is in AP mode. But mesh will give you better Wifi experience moving around your home between units.

YouTube ads are embedded these days and you aren't going to be blocking anything. Anyway, you're worried about PlayStation ads but not the millions of actual videos you can get to if you watch long enough and go down the rabbit hole.

Mesh still needs good signal strength between the units, so it may take some playing around with placement. But in general, it will give you better speeds further out, and better signal strength with less drops. Think of it as a middle man to pass the signal further down from your main unit. So you can't just put one in the same room where you get 30Mbps and expect good results. If you keep that in mind, you can definitely get decent results. Still not as good as wiring your PC as it is still Wifi.

The TPLink Omada line is great. Switched from Ubiquiti a little under 2 years ago. Affordable, reliable, and just as easy to work on. Better availability too, though maybe not as bad now.

It sounds like you have 2 routers? You should only have one router, and the other would need to be in AP mode. Or maybe Spectrum is just sending you a message to play better games.

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.

If you can't put it in bridge mode or get a modem only from the ISP, not sure you'll notice a difference. If you are currently on Wifi, then wiring your PC will be best. You can always put a switch after their modem/router if you need more ports for devices. But adding a router will probably not make anything better. The ISP should give you something that is capable of the speeds you pay for, and wiring any device will be best.