Classic/Antique Car Repair: Starting a 54 Bel Air that has been sitting, water check, gas tank

Question
When I bought this car, I was told that it has been sitting since January. He
said that the water pump needed to be replaced. I did that, as well as
replacing the spark plugs (including adding mystery oil) emptying the gas
tank and replaced with new gas and a cleaning additive after following advice
to add more fuel and an additive to the existing gas, and try to start it up,
which resulted in a varnish smelling smoke. I replaced the battery and cables,  
drained and refilled coolant and oil, cleaned the air filter (and is there a fuel
filter to replace or clean?) and tried to start the engine putting a little gas in
the carb. It starts each time I put gas in the carb, sometimes without, but it
dies after a few seconds, sometimes after letting off the gas pedal,
sometimes after I stop turning the ignition. The last few times it has made a
loud popping noise as it abruptly dies. I am not sure what this is and whether
it is because I didn't replace the fuel lines (as they were unhooked when I got
the car) or because initially I followed advice to just add more fuel, or
something else entirely. . .

Answer
As you have already determined, that was bad advice. You now have a bad mixture in your carb, including water. Check for copper filter in fuel line inlet to carb (large fitting fuel line goes in)

Probably going to have to open carb and clean (may be ok to just open top, combined with heavy specific carb cleaner spray)

If engine dies only when you let off key, that is another issue.