I have a 1993 s model with a d15b7 swapp. It’s got some cheap autotune see through distributor on it that clearly don’t look factory! During cold starts I can get the car to crank up perfectly (other than the bogging for about 8 seconds till the motor gets going. Now I can be driving perfectly fine and boom the car backfires puffs an dies out. And when I go to crank it back up it takes a while to start hit or miss. Now it doesn’t do this all the time it’s literally a hit or miss when I drive. Should I be focusing towards the distributor?

 

That AEM clear distributor cap could be the problem. It's a bit gimmicky and does not last nearly as long as stock cap and rotor. The center button on the cap wore out on me in about 4 months. It could cause miss spark when it gets bad enough.

Do a basic tune up (Plugs, Wires, Cap, Rotor, and Valve Lash) to see if it clears up.

If you just acquired the car, it's also HIGHLY recommended to replace the timing belt and water pump so you know right where it's at for condition and mileage on the belt and pump.