There is a small battery in the CPU (? - I believe this is where it is) that keeps power so the BOIS settings can be 'remembered'
In reality the simplest solution would be to line the inside of your computer with tinfoil. This would prevent an attacker from being able to receive any signal your computer is transmitting, as well as to prevent you from looking crazy.
Not in the CPU, it's a separate component on the motherboard.
Lining the case will not help if it is the cable to your monitor that is leaking the RF. So you would have to wrap the foil around that cable, and earth it.
Or you could put another, very noisy, RF setup in the same room.