1990 Buick Lesabre Hesitation

Hi ranjoman, Welcome to 2carpros and TY for the donation

Start by checking and testing the TPS and MAP sensors and get back with some results we start here

NOT SURE WHAT tps IS, BUT WOULD'T THE CHECK ENGINE LIGHT COME ON FOR A MAP SENSOR FAILUR. ALSO, FORGOT TO MENTION, I REMOVED THE THERMOSTAT

It'd be nice if the computer tells us all the time when any of the parameter sensors and actuators has a problem but this is not the case, also at times it will pop a code/s and there's nothing wrong with the trouble area. On the thermostat removal it will caused the computer to lock the fuel loop control on open loop and giving it fuel at all times due to the coolant temperature sensor unable to provide the computer the correct input signals to control fuel

Okay the TPS is the throttle position sensor and the MAP is the manifold absolute pressure sensors check and test these 2-sensors and tell me what you got.

Please! explain this and lil bit confused here:

take it back into town, it is back to smooth again. If I drive around town, stop and go, it goes back to hesitating.

Here's my checklist on what could cause hesitation/bogging/jerking problem:

Oxygen sensor.
Catalytic converter.
Fuel injectors dirty/sticking.
Mass airflow sensor/Airflow meter.
Throttle position sensor.
Manifold absolute pressure sensor.
EGR Valve
Fuel pressure regulator leaking,fuel filter or defective fuel pump.
False air leakage.
Fuel contamination.
Foul/defective spark plugs.
Open spark plug wires.
Ignition coil/Coil packs defective.
Incorrect ignition timing.
Cap and rotor.

Note:If it doesn't apply disregard.

Could it be a weak alternator? I notice the voltage indicator light
'faintly" illuminated upon start-up. I read that this could be an indicator of a weak alternator. When rpm is high it works stronger?, when rpms are low, weak firing to cylinders?

Could be the alternator if its not producing the correct output voltages, sensors and actuators needs the correct voltages to operate properly-get it checked out and also check the drive belt tension