Every time i turn my car off, rev too fast or shift i get "gunshots" and i think my neighbors are getting angry so i wouldn't mind if Anyone could help me... and my muffler blew up

Backfiring usually indicates a timing problem.  You'll need to investigate things like engine timing, belts, and distributor.

Backfiring during a shift after revving it up is indicative of a small exhaust leak somewhere in the system. When under a load, the exhaust system has pressure. Usually 1-2 pounds. When you let off the gas, a small amount of vacuum in the exhaust is now present. This vacuum sucks in cold air through the leak and it's now getting 'instantly' heated by the exhaust gasses and expands rapidly.  The expansion builds high pressure and when it exits, you get a 'backfire'. If you can't find a leak by listening, use a long piece of fuel line with one end to your ear and use the other end to probe around exhaust system unions. Or just get a mechanics stethoscope from the auto parts store.

I believe the leak is at the exhaust gasket in the middle of the car.... or the muffler that has been split in half

My car does the exact same thing. We narrowed it down to it's running rich, meaning it's getting too much fuel, so it can't burn it all which means some escapes into the exhaust system, and when you shift the change in rpms can cause your engine to shoot flames, meaning that it can ignite the fuel particles that have collected in the exhaust system. And there is no lean rich adjustment on ea82 carbs, you have to re-jet it. My local subaru dealer can't get jets even.

Just my 2¢, hope you figure it out,

Tom

I don't know if this helps any but i have an EA71 with a Weber carb and a manual fuel pump(has to be turned on after the car starts)?

a manual fuel pump?    I'm guessing this is an electric fuel pump?    with a manual switch.

Check your timing.

Install fuel pressure regulator before the Weber.

The backfire is unburnt/extra fuel in your exhaust, that then ignites when it gets hot enough or finds a 'spark'...

Alright. Thank you

Backfires come out of the motor, carb or intake.  afterfires are what comes out of the tailpipe.  just mentioning it in case your googling, that will turn up better info.

 

basically its a combination of extra fuel and fresh air getting into the exhaust.  air + fuel + heat = boom.  you cant keep your exhaust cool enough, and almost all motors will output some straight fuel into the exhaust, so work on cutting out the air in the system.  any exhaust leaks need to be fixed, but if you have the ASV system on your car then that could be causeing the problem as well.  on mine the plastic baffles were leaking and once I plugged off the hoses it completely stopped the afterfire.