Have you replaced the seats and the washers and stems if required? Have you do it properly? If so you have done everything possible and the valve itself is no good and it should be replaced.
Hot because the hot will burn the germs off of your body
a cold shower
pressure regulator valve gone bad . stem problem or seats in faucet
Yes (with the exception of absolute zero) but the energy in hot and cold is always heat energy. (Cold is defined as the absence of heat)