Car died while driving. Electrical seems fine.

When was the last time that the carburetor was stripped and cleaned? Also have you checked the fuel filter? Finally, the problem seems to come and go as the engine is run (and it gets hot) check that the fuel line and any electrical cables are well away from the hot engine as far as is possible.

Replace the power steering belt. Make sure that it is tight.

I had a 92 that suddenly lost power and I could not keep up with freeway speeds. It turns out the mass air flow sensor failed. When it fails it has a "Limp Home" mode that allows you keep the car moving and not leave you stranded.

what makes you thing the tires/wheels tighten (felt by hand off ground?)
my guess , you meant it seems. like???
1: lost engine power?
2: transmission not up shifting?

is this a auto A/T or manual M/T tranny,
if A/T , you need to look at the engine RPM when you lose
power (acceleration on demand)

RPM rises, car dont move faster ,this is tranny slip.
RPM fails to increase, and speed, up hills. this is called lost engine power.
lost engine power can be caused by , bad spark (tuneups skipped?)
or weak fueling.
weak fueling too can be cause by skipping the fuel filter step in the tune up list.

Sounds like the catalytic converter is shot..

I'm not sure of this, but my friend experienced similar situation.
He had a Kia Pride used for Taxi cab. He have replaced damaged parts, replaced freon for his aircon and overhauled the engine. The cab really runs smoothly and in good condition.
But from time to time, the engine stops. Just like you, everything is normal, but stops unexpectedly. We even have it checked from my friend mechanic and said that everything is normal. He gave up the car and he loosed around PhP50,000.00 at that time (enough to pay rent for a year. He later found out that the car runs OK again...
THE NEW OWNER HAVE THE WIRING AND ELECTRICAL CIRCUITS RENEWED!
And a car owner claims for the same problem, I said its ELECTRICAL CIRCUITS, it should be replaced. When she have it fixed, the mechanic have her car's wiring replaced. And it runs smoothly again.
Please try...

Check the battery and alternator wiring connections. Also, check the alternator belt. If it is missing or has no tension, the belt tensioner may be broken. The thumping seems to imply a catastrophic mechanical failure or a small explosion affecting the electrical system, but it may have been unburned fuel igniting in the catalytic converter due to a problem with the engine computer (perhaps it wasn't working right due to the electrical problem).

could be a lose ground somewhere. check the wires from your batery and alternator. specifically the grounds. no ground no power.

If ignition and spark seem to be ok, it's time to look at your fuel system. When you say "turns off", if all electrical power seems OK, check the fuel pressure for faulty pump, plugged filter or faulty regulator.

Will it start when you give it a jump or install a good battery? If it does the problem is your alternator. What most likely happened is the alternator quit working while you were driving and the car was relying on the battery directly to keep it going in which the battery completely lost power and shut the car off.