Is it a shitty cable?
1sh0t1b33r
With most ISP's, you only get 1 IP unless you have a business account. Plugging in a switch so you can run extra WAN connections to a router will not magically give you extra speed.
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.
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.
Probably a bad cable somewhere as long as the router, switch, and device are all Gigabit plug ports.
Lazy electrician or cheap homeowner?
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.