The primary reason for gas over flow from the carburetor is a stuck or failed needle seat valve.
This vehicle does not have a carb. The fault is likely with the mass air flow sensor or something of the like.
On a 1985 Chevy Celebrity the mass air flow sensor relay is located on the strut tower on the drivers side of the car. It is behind a cover. The fuse for the mass air flow sensor is also there with the relay.
Clean out the carb and add a high flow air filter
It backfires because it's lean. The trick is to figure out why. Check your vacuum lines and anything that could obstruct fuel flow.
Without an air vent the fuel would not flow to the carb.
The mass air flow sensor is in the air duct between the air filter canister and the throttle body on the plenum.
you would need a fuel pressure regulator to control the flow to the carb to keep the pressure about 5 or 6 PSI, you shouldn'rt have to do anything with the pump in the tank.
Bad needle/seat valve in carb.
The most likely reason that the heater control won't change the air flow is that the cable that moves the diverter valve has broken and will need to be replaced.
check the air flow sensor at or near the air cleaner. could be unplugged or faulty, engine will run a few seconds then stop.
Its a very easy process. All you need to do is locate the carb and take it off. Take the float bowl off, but some carb cleaner and take the float out.. Clean all the points and follow the flow of gas through the carb. once you have resolved the flow of fuel, and cleaned any gunk out, put back together and away you go.
The computer doesn't control the fuel on a carb. engine, the carb. does. It also controls the air flow. So putting a new carb. on will not affect the computer. The new carb. will do everything by itself, but you will still be limited to the amount of fuel your pump can spit out and the amount of air your air intake can suck in. Then the exhaust comes into play because you can only get enough power as your exhaust system allows. To answer the question though, yes you can upgrade your carb.