Why does my car cut's out when am driving and have to wait 20 minites to start it again

If you have no trouble lights and the car is displaying these kind of problems, why don't you return the car for repair ?

I would bring the car to a auto zone and have them but the car on the computer for a diagnostic check.

Also, if the car will not start after running, does it back fire or seem like its being choked out ?
Could be a fuel problem or restriction. ( FPR, Fuel Pump, Filter ect.

Could be crank shaft sensor.

Try getting your transmission solenoid replaced. After I got mine replaced it ran fine after that. That's the exact same thing my Lumina was doing.

Normally the problem is electrical, something gets hot and looses contact. Could be a relay, coil, sensor, or several other components.
When it will not start you will need to figure out if you are missing spark to the plugs or fuel to the injectors to proceed.

Check behind the distributor cap and see if the cam cover seal is leaking. When that seal leaks the car will drive fine til engine heats up the oil and it starts fouling out the distributor cap and rotor. When it cools down the oil hardens again and car run fine. I would start by looking there.

Most probably cause over heated check the radiator water but
DO not open its cap while engine running
or hot wait till vehicle cool down and also check the engine oil as well good luck

relay problem either the asd relay or the fuel pump relay is bad. now pay me

Don't rule out fuel pump. Had a 95 do the same, ran great when cool in morning then when it got hot in afternoon, it would quit. Wait 15-20 minutes & go again, sometimes got me home, other times a few more miles until it cooled down again. Luckily I had access to a fuel pressure gauge. Cool in morning had 49 psi, when it quit, 2 psi. Wait 20 minutes, 49 psi again. If you can drive it around until it starts to act up then run into a repair shop for fuel pressure test it will confirm it. If not, they may need it all day to monitor the fuel pressure & confirm it is pump. If your a gambler, change it & fuel filter. One thing I did get was trouble codes indicating a lean mixture, due to starving for fuel. Have you cycled your key to retrieve any codes yet?

Hello it hapend to me with my car i just replace the crankshaft position sensor !!!

i would check your ignition system. you would need a meter for this but look for broke or loose connections. if it was a fuel problem i dont think it would just start up after 20 minutes. or you might try your ignition switch. if its shorting or something then ya well it would cut your engine off real quick