Engine shuts off when AC is on in slow traffic

#1
I own a Toyota Corolla 2010 1.8 model. My Toyota is not U.S made. It was made in South Africa. Imagine this scenario;

When my car is stationary in traffic (not in park position) or I am driving at very low speed like in a traffic Jam.

If my transmission is engaged (D or R position) and my AC is on. The tachometer (RPM) needle keeps fluctuating which causes my engine to vibrate vigorously then suddenly the needle goes down to Zero and my Engines shuts off on the road.
I have to switch off the AC, put my transmission stick in park position and restart my engine before moving forward again.

However when I am driving at a cruising speed and the AC is on this does not occur.
This only happens when my car is moving slowing in a traffic jam.

To prevent this from happening when I am moving in slow traffic.
I either put my transmission stick into the Neutral position while the AC is still on or I switch off the AC completely.
In both circumstances, the RPM needle does not fluctuate badly, the engine does not vibrate vigorously and does not shut off.
When time comes for me to accelerate, I switch on the AC again.

I purchased this vehicle fairly used and the factory fitted automatic AC compressor unit was removed and a manual compressor was fitted in its place.

The electronic throttle body and MAF were recently replaced. However the replacements were also fairly used parts.
Difficult to get brand new parts in my region.

In trying to solve this issue I have replaced ignition parts and associated sensors

Scanners don't reveal any new internal engine or transmission issues.

I want to know if it is the AC that is affecting the engine and causing it to shut off or if it is the engine itself that is the problem and should be replaced or if the throttle/MAF are still not functioning properly thus I need to acquire new ones instead of fairly used replacements. Or is it a transmission problem.

I want to add that when my transmission is engaged in either D or Reverse position, there is a slight vibration from the engine area which I can feel on my driving seat.

I know something has to be replaced in this car to make this stop. I just don't know what it is.

Can engine parts for US built 1.8 engines also be used to service my engine? It is easier for me to get new parts from the U.S because a lot of auto parts stores have websites.

Any help is appreciated
 
#2
I just want to add that the factory fitted automatic AC compressor unit was already removed and a manual compressor was fitted in its place. I simply serviced the AC as is. I did not return the AC to its factory system.
 
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