Does the son have a mobile phone? Turning off wifi access to the router won’t stop them from using mobile data

You need a Modem & and Router before thinking of getting a wifi extender. Eeros have a nice app if its important to you.

And what devices are you seeing the slow wifi speeds on? Your connecting to a 5GHz network correct? 45mbps sounds like 2.4GHz WiFi.

That cable shouldn’t affect your WiFi… But it would certainly affect your internet.

HUGE no. That’s asking for the cable company to shut you off or come knocking on your door. You would be causing ingress and prob tick the neighbors off too. You’d be injecting AM/FM/OTA TV and whatever else is in the air into the cable system.