Aniefreez and gas problems

Sounds like 2 issues, first heater core leaking maybe you can bypass it until you can replace it, second the EVAP System needs looked at, May be a purge solenoid or EVAP cannister or some other EVAP issue.

there's a vent problem with the filler neck , they may not of included a smaller vent tube in that beast , or someone got rid of it instead of replacing it , pump the gas slower

We're talking 1956 Belvedere ,,,the engine controls consist of a Carburetor, a mechanical fuel pump and a gas pedal ... this car was built when the vacuum tube was still dominant in radio's/TV's.... Are you certain the gas gauge is accurate ? Perhaps you think that you need gas when the tank is almost full ,,,,If you raise the hood and look toward the back of the engine compartment ,, you will see 2 hoses at the wall separating the engine from the passenger compartment .. you need to take those hoses off and join them together using a small piece of copper pipe ( 1/2" should do it) and 2 hose clamps ... you have bypassed the heater and you can now expect to freeze your butt off

BTW ... If that car is not full of cancer and in reasonably good condition ,, you may get a lot of money for it ....after all ...it's a 61 year old car

How much you want for it , is it posted ? You , or someone , needs to go through this beast to get it right before you go out driving .It'll save you a lot of trouble .