Will not start battery and alternator is good will only start if jumped and shuts off while running after car is jumped started.

taking the battery leads of a running alternator is one sure way of destroying the alternator
if you think a battery is dead you have it load tested and replaced if it doesn't meet the test
what you should be doing is taking the vehicle to an accredited auto electrician and having the battery load tested and the alternator and voltage regulator professionally tested for proper operation

Well, that doesn't look good, but I can not see that shutting your engine off.

I suggest that you have a load test done on the battery as from your description there is a dead cell . Coming to a stop is when the engine is idling and the output of the alternator is below that required to supply current to the ignition system. With a dead battery and jump starting it is possible that the CPU program is corrupted so after you fit a good battery use a scanner to reset the CPU program

you mentioned new alternator and battery, but it seem that the alternator is not charging, when you install the new battery the car started and run and after hours of running specially if head light is on the car shuts down. this is an indication that the alternator is not charging. (factory defect) have it checked or return part to auto supply.
if alternator is good and you have the car jumped and run it will not shut down even if your battery is dead because the charge of the alternator is enough to power the electrical system of the car until you turn it off. this applies to all cars

check voltage from battery car running. if alternator good it will produce 13.6-14.2 volts. if lower replace alternator. good-day ! make sure battery posts and wires are clean and tight.

Check for loose battery terminals. Car will not start without jump because battery is not connected properly. Starter is probably good or car would not start with or without jump. If alternator is bad and not producing current, car would die after running a short while as battery would out of juice and without alternator current the car would die - so probably alternator is good. If connections are all good, get a voltmeter and test the battery voltage - it should be over 12.75 volts. If not, battery is not holding charge.

Probably the battery. Car wouldn't run if the alternator didn't work, it'd run until the battery drained and then stop.

its the battery. the battery holds the charge and the alternator charges it so when you jump the car it stays running because you alternator is providing power when you shut the car off you have a bad battery that isnt holding the charge needed to start it again.

Sounds like your battery has gone south. If you can jump it to start and it continues to run then it is just running off the alternator. The battery can no longer store power. That is why you can't get it to start when you turn it off. It requires an alternate power source to crank the engine until the alternator kicks in to power the ignition. Have the battery load tested with a good carbon pyle load tester.

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.