Someone has either reversed the wires on the temperature gauge or damaged the wires from the engine to the gauge and spliced them back backwards. It is a simple reverse of polarity.
First, check your thermostat, your car may actually be overheating slightly due to the thermostat sticking. If it sticks then no anti-freeze flows through the heater core(providing the cab with heat), which will cause overheating. If it eventually opens, allowing flow, and cooling off the fluid/engine (gauge drops) then fluid flows again giving you anti-freeze through the heater core and heat pours out. Check it by removing it and putting it in a pan of water and boiling the water with a thermometer in the pan (try to hold them both off the pan surface with tongs, it may screw up your reading), watch close for the temp at which it opens, should be 180F, but check for your car.
Second step would be to check your water pump, low flow from a water pump could also cause the same problems.
After those two, "you're on your own kid"
It would be better to write: My gas gauge reads empty. Note that 'gauge' is singular, so it needs the singular verb, reads. If you had several cars all with gas gauges that read empty, then the verb would be read.
This would indicate that the system is low on coolant when the gauge is hot. Not enough coolant to service the heater core.
If your gauge is normal your thermostats okay, so its got to be your heater core. Usually located behind your dash board. Easy to swap just a pain to get to. Or it could be your gauge is out and your thermostats bad, but usually a couple gauges would go out with them. Hope this helps a little.
I would suspect the sending unit in the gas tank is at fault.
If you are absolutely sure you do not have air trapped in your cooling system then you may have a defective gauge if you are getting heat through your heater. Usually I would say you have a coolant flow problem with either a stuck thermostat or a bad water pump but if you have heat from your heater, then you must have circulating coolant in your system. I would check the gauge or the sensor.
A stove is a two pole 50, and hot water heater i would recommend the same.
A major clue would be the vehicle stopping.
i would recommend getting gas when that happens. perhaps take it to the mechanic to fix the gauge
check the connections behind the gauge they could pop loose
The thermostat is the most likely culprit. The major clue is that the engine temp stays in the lower middle of the gauge - the heater core would not cause this. The thermostat is most likely stuck in the open position - needs replacement.
If the coolant level is okay, I would suspect a restricted heater core. Try flushing the heater core.