Why would my TV image turn black when electrical appliances turn on?
I agree with DMoore that the flickering is almost certainly caused by a voltage dip when a large appliance turns on. A fridge can easily pull 1000+ watts momentarily as the compressor starts.

If you want to verify the voltage dip you can do so with a multimeter with a "MIN" function. Insert the multimeter probes into the outlet that's giving you trouble, set the multimeter to "voltage (AC)", and enable the "MIN" mode, which will remember the lowest voltage it sees. Then wait for the fridge to turn on. Typical US household voltage should be in the 110 - 120 V range. A voltage dip much below 110V could definitely cause flickering.

If the devices are on the same circuit, the easiest thing to try would be putting them on different circuits. You could also call the electric company to see if they have any thoughts.

If you don't want to do any electrical changes, you could also get a voltage stabilizer to plug your TV / home entertainment system into. It's basically a fancy surge protector that will even out momentary irregularities in the household voltage current. Many battery-backup power supplies ("UPS") also include voltage regulation.

Edit based on question updates:

The same circuit means that the outlets run back to the same circuit breaker in your breaker panel. The easiest way to figure out if they're on the same circuit is to flip off the switch to the refrigerator and see if the TV also goes dead. If your circuits are not labeled, this may take some trial and error.

As for a surge protector: they won't help with under-voltage at all. Surge protectors cut the power when the voltage gets far too high (typically 300 V or more), but don't do anything when the voltage is too low.