All kinds of ugly . . .

I am having a few issues with my 96 sohc neon. First and foremost it really hates not having the accelerator depressed, if i let go of the pedal it dies. Second It really hates having the A.C./Heater on, when its on it sounds like heavy breathing or whirring, everything struggles, lights dim and the engine kindof trys harder. Ill leave it there for now. I could really use help here!!
Thx Tonnes!

First, check your alternator voltage output. With engine running put a volt meter on the battery posts (+/-) and check for at least 14.1 volts DC. Second clean those battery posts good. How is the battery, is it new?, same test as the alternator but with engine off and you need to see about 12.1 Volts DC.

Battery is good charge, alt is producing well. I changed my spark plugs, used some fule injector cleaner through my gas. Would a defective fuel filter cause an issue?

A bad fuel filter will slow down accelreation. You can put a pressure gauge on the fuel rail in engine compartment and look for about 45 psi at idle, if you have that, all is well. Try this, put a couple of bottles of water out or dry gas (any parts store) into the fuel tank, I have had many instances where condensation in the fuel (water ) would really screw up my cars running.

I have been told it will shut down my engine completely. It only stalls after I have driven for about 45 or so. Overheating fuel filter
I also have a gauge problem, My tanks reads as empty when I have 3/4 of a tank or less.

The fuel gauge issue is probably a bad sending unit. The sending unit is in the tank attached to the fuel pump and acts like a float to send the fuel level signal to the gauge. A new pump (with sending unit should solve this problem).You can buy the sending uit separaately and replace the old one, but since you are already at the pump, a new pump/sending unit seems more pratical (albeit more expensive as well).