Why do I need to pump the gas pedal to get the 83 prelude started

Cheque for disconnected vacuum hoses. sometimes this happen after working around the engine, if everything looks good, start the engine press down the accelerator pedal keep the engine running about 2500 rpm for 3 minutes then let the engine idle, if the engine idle this means you need a new idle speed control motor, if the engine still dies most probable the fuel pump it's going out if you have a code reader it's possible you have some codes and this can give a good direction

make sure spark plugs and wires been replaced.replace distributor cap and rotor.replace fuel filter in the carburetor in let nut to fuel line.also check carburetor automatic choke plate make it closed during start up and open as engine warm up.but the choke need to closed when you first start engine up in the morning. i had same car years back you had to pump accelerator pedal twice then start engine. had be careful easy flood out carb engines.

Check the fuel pressure, could be the fuel pump

We do not have this model in US, but I assume it is a new model 2016-17. You throttle (and the "rev" ) is controlled by the computer. The fact that your car is idles - should mean that your computer is fine! There are two types of idle control: 1st- when you have a bypass of the throttle, which lets the throttle flop stay close while idling and let's the air into the motor through a bypass and electronically controlled idle switch. Inspect your throttle - the electronic/metal unit located on the large pipe through which the air gets into the motor: if you have a "bypass" for the air then you need to inspect your throttle body as it could be your problem.
2. most likely you do not have a bypass and your idle is controlled by your throttle body, then it is sure working fine and your only issue is that your engine computer does not know that you press the accelerator. Your gas pedal has an electrical unit on it which connects to the engine computer- inspect the connector/wires if all looks fine most likely your accelerator sensor does not work- you need to change the gas pedal unit ( I think it called accelerator sensor).
Good luck.

Could be one or both of two things.

1. The accelerator pump in the carb is clogged, the linkage is unhooked, or the diaphram in the pump is bad. It's cheap to replace and comes in the carb rebuild kit. This usually just causes hesitation when you step on the gas pedal. It doesn't usually cause the engine to stop running.

2. More likely is that the main jet in the carb is clogged. At idle, high vacuum under the closed throttle plate in the carb causes fuel to flow thru the idle jet. As the throttle plate opens (as you step on the pedal), the vacuum under the plate dissipates, stopping the flow of fuel thru the idle jet, and the vacuum ABOVE the throttle plate increases, which is supposed to then draw fuel from the carb bowl thru the main jet in the carb. If the main jet is clogged with dirt, then it can idle just fine and die as soon as you step on the pedal.

The car needs a general servicing

Have you scanned for fault codes? How about the Throttle position sensor, have you tested it?

DIRTY INJECTORS OR SPARK PLUGS FOULED OUT.

i think the dist is adjable try advanceing it some times the after market caps are a little diffront

I need to get a clear mental picture of what exactly is happening.

With this said, you stated that the car "runs fine" until warmed up.

Q: When you start the car when cold it idles fine?
Q: If you allow the car to idle until "fully" warmed does the car stall?
Q: As the car begins to warm up, Does the RPM fluctuate abnormally?
Q: Does the car Only stall when you press on the gas pedal or does it stall just sitting and idling in addition to pressing the gas pedal?
Q: If you can drive it while cold does the car stall during acceleration when warm or only at Stop Signs / Lights?
Q: If you wait 20min or so, can you start the car again?
Q: How many miles are on the car?