Engine stop after running 30 to 40 mins. Start back but only cranking. Wait about 30mins to 1 hours then can start. Engine symbol Display defective light still 'on'.

I would suggest checking the fuel pressure when the engine dies. You may have to buy a fuel pressure gauge and carry it with you, or see if letting the car idle for 30 min will duplicate the problem. Could be a fuel pump or relay.

possibly faulty crank angle sensor.

Check the fuel pressure.

to to a higher grade of fuel it might just stop pinging

Wouldn't think sensor or computer problem , more likely an ignition module . When it dies pull a plug wire an check for spark ,i think you will find no spark . Just from my 30 years of diagnosing GM vehicle's this has been the #1 cause of a start an run till warm an dies an wait 20 min . to an hour an it starts again problem. But without testing to know for sure that would be a guess . Having a qualified an certified repair technician diagnose the problem is always the best idea.

fuel pump probably defective.. it's inside the gas tank

I am having the same problem. did you figure out what was wrong with yours. I have tested all of the wires in the harness under the dash, they r fine. I pulled off the starter and had it tested; O'rilies said it was fine. It is a 5 speed, and I can push start the car just fine any time. Like yours, some days my car starts, some days it doesn't. The days it starts, it runs fine with no problems starting or running. the problem is the days that it wont start.

Your problem is cranckshaft sensor or fuel pump!

Do you have a Wankel engine in you car?
Then you have a flooded engine.
Pull the fuel pump fuse or relay and crank the engine over......until it starts then stops.
Now put relay or fuse back and start.
You cannot start and stop a Wankel in a Mazda RX when it is in it's cold mode and restart it easily.
Always run them for at least 10 min before shutting it off.
The other way to start after flooding.....is wait a day.

It may be a bad ignition mod,, Autozone test
are OK for batteries and Alternators but not
modules because it's not a real test, mostly
continuity test, not component heat test...
Get a new module and try it...