What is causing engine stall? While driving.

Check fuel pump pressure. This sounds like vapor lock.

Remove the fuel And try driving the car does he do the same thing?

Remove the fuel cap, does it do the same thing?

Actually, yes, it can be vapor lock. Check the fuel pressure. Vapor lock doesn't occur until heat builds up enough to boil the fuel in the fuel lines.

Not necessarily. The pump could have cooled down enough to provide adequate pressure and the engine compartment could have cooled down enough to keep the lines from boiling. Be sure the check the pressure once the vehicle reaches operating temp and right when the problem surfaces.

Aside from letting them have it for a few days and filling the tank for them, asking them to idle it and drive it while carrying a fuel pressure gauge? Not really.

What I would recommend is carrying both a fuel pressure gauge and a multimeter or test light with you for awhile. When the problem occurs, check the pressure and check for voltage at the pump.

Is this something that happens on cold and hot days, or just hot days, or just cold days?

You should be able to borrow a fuel pressure gauge from places like Autozone for a few days. Also, like I said, get a multimeter, or at least a test light to check to see if the fuel pump is receiving power when the problem occurs. It could just be the pump or relay overheating.

Are there any specific times and conditions where it happens more often?

Unless you live somewhere where there are no chain parts stores, you can either rent or borrow a fuel pressure gauge. Even though I strongly feel that this is either a case of vapor lock or overheating fuel pump relay, I will run down the other possibilities for you:
1: Overheating ignition contacts in the ignition switch.
2: Overheating coil getting ready to fail.
3: Overheating relay set in the ignition system.

All of these are easily actionable items. Relays and ignition contacts can be easily tested with a test light or meter. Fuel pump pressure is easy to test if you go rent or borrow one from a parts store such as Autozone or Pep Boys.

Each piece of advice you were given was 100% usable. It's not our fault you don't want to believe it or try it.

Just go to the parts store at buy a can of starting fluid. When it quits spray it in the intake if it starts. It is starts you have a bad fuel pump or fuel regulator that will help you from buying a pressure gauge. If it doesn't start then you would need to investigate is there power to the injectors, let's start here