Car starts and stalls

If I remember correctly that Jeep had a mechanical fuel pump attached to the engine. I suggest you disconnect the fuel line before the fuel filter and put a pressure gauge on the line. Crank the engine for at least 15 seconds and go see if you have at least 7 lbs of pressure. If not, you need a new pump. It that was good, now disconnect the line AFTER the fuel filter and see if you have a sufficient volume of fuel coming out. For that I suggest you have someone else crank the engine while you hold the hose in a pail. If the stream is weak, change the filter, reconnect the line and see what happens. If it still starts and stalls it could be a clogged carburetor.

Did you do a spark check by holding the plug wire away from the engine while someone cranks it? With a spark plug in the wire, hold it at least 1/2 inch from the engine while someone cranks it. That spark should be able to jump off the plug and into the engine. If not, you have a weak coil. If the spark is strong and you have the correct plugs installed, then it almost has to be the carburetor.

Good luck with that, I have fond memories of older jeeps.

MAF mass air flow sensor.

A it's starting to run rough and stall what happens if you spray a little carb spray into the throttle body? Will the idle smooth out?

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Check your spark plugs , wires , fuel filter ,and the get back to me

It could be many things.
When the engine crank but won't start
Retrieve PCM faulty code if any.
Engine need 3 things (Fuel, Air, Fire (spark)
1- Fuel = fuel pump working during the problem you can hear a sound at the fuel tank cap (remove)
All Fuel Injectors working.(Power and the spray).
2- Air = MAF defect (Mass Air Flow) no code will be set
When the engine is running with a screwdriver lightly hit the MAF the engine will stall if it's the problem.
air filter restrictions
3- Fire= Is there spark at all spark plugs wire?

Find out the ground of power windows it could be the same as fuel pump or ignition system (Ground corrosion, high resistor)
and many more.
See good technicians to fix your car..

Hope it helps

check your grounds. I find many easy fixes by cleaning all the grounds around the engine bay. I would also check the ground at the fuel pump connector that wiring is prone to corrosion and breakage

Fuel pump is where I would check next. Your mechanic can do a fuel pressure test to verify this is a fuel problem.

Have you ever heard of testing before replacing parts ? Fuel pressure an flow tesing , testing the electrical circuit for the fuel pump , amp draw testing , voltage drop testing etc... Thier are no magical fixes in auto repair . No spark ! check B+ voltage an ground circuits for the ignition system , Ignition System Designs Operation and Testing an SD Premium video

When you stop if the Mazda stalls try putting the car into neutral gear and see if it still stalls. if the Mazda does not stall in neutral then the torque converter has failed and needs replacing.

You've already eliminated the spark plug & wireset, distributor cap & rotor.
Sounds like your car needs a tune-up, specifically, the PCV (positive crankcase ventilation) valve, and/of the EGR (Exhaust Gas Recirculation) valve.

Components checked/replaced during a tune-up are:
air filter
motor oil
motor oil filter
breather filter
fuel filter(s)
fuel strainer
PCV valve
EGR valve
spark plugs
spark plug wires
ECM or distributor cap & rotor
cabin air filter
transmission oil filter
transmission oil
engine coolant
check all vacuum hoses and lines

Troubleshooting the no-start condition - from the 1990 Mitsu Mighty Max Repair Manual:

Priority Action Part Type -- Cause
1 Inspect Battery -- Battery Discharged or Faulty.
2 Inspect Battery Cable -- Corroded, Broken, Shorted or Poorly Connected Battery Cable.
3 Inspect Distributor Cap -- Distributor Cap Cracked or Burned.
3 Inspect Fuel Filter -- Clogged or Dirty Fuel Filter.
5 Inspect Ignition Coil -- Faulty Ignition Coil.
6 Inspect Wireset -- Worn, Damaged or Faulty Spark Plug Wire(s).
7 Inspect Spark Plug -- Incorrectly Gapped or Fouled Spark Plug(s).
8 Inspect Starter -- Starter Motor Faulty.
9 Inspect Fuel Pump -- Low Fuel Pressure.
10 Inspect Solenoid Switch -- Faulty Starter Solenoid Switch.
11 Inspect Fuel Pump Relay -- Faulty Fuel Pump Relay.
12 Inspect Fuel Injector Pressure Regulator -- Faulty Fuel Injector Pressure Regulator.
13 Inspect Ignition Switch -- Improperly Connected or Faulty Ignition Switch.
14 Inspect Starter Drive -- Faulty Starter Drive.
15 Inspect Fuel Injector -- Dirty or Worn Fuel Injectors.
16 Inspect Fuel Pump Strainer -- Clogged or Dirty Fuel Pump Strainerat.
17 Inspect Engine Control Computer -- Incorrect Operating Information Being Delivered and Sent From The EEC.
18 Inspect Fuel Tank -- Fuel Tank Empty.
19 Inspect Carburetor -- Carburetor Flooded or Faulty Choke.
20 Inspect Distributor -- Worn, Loose, or Incorrectly Installed Distributor.