You get Radio Frequency Interference when you plug into the cable, the TV, or the phono.
All are separately grounded interfaces.
Your solution with the turntable is to experiment with the grounding. There is no "right way" to do it; fear not. Is there a separate ground lead from the turntable to a ground lead on the phono preamplifier on your receiver? Does the turntable have it's own phono preamp built in?
As for the video, you can kill the ground loop with a transformer. Do you connect the cable to your receiver, than connect the receiver to the TV?
An antenna is simply a piece of wire of a certain length. Without going into details, for every radio signal there is a specific length of wire that will act as an antenna. Your first solution, then, is to change the length of the cables you use to connect everything up.
Don't bother with the speaker wires. They are very much unlikely to be the cause of the problem.