Regarding choke, adjust the manual choke by pulling the cable so that it's in the closed position with a cold engine and in the fully open (vertical) position in a warm or hot engine.
(1) The choke should be fully closed only with a cold engine
and when the engine is not running. A fully closed choke will even stall a cold engine. It's only needed to
start a cold engine and then it should open immediately to the proper angle (see below) when the engine starts running.
(2) As soon as the engine starts running, the choke should open to about 38 degrees from horizontal when the coolant temperature is below 12 C (Celsius), about 55 degrees from horizontal when the coolant temperature is above 12 C, and 90 degrees from horizontal (fully open in vertical position) when the coolant temperature is above 59 C.
You may need to close the choke first by kicking the gas pedal to the floor once or twice before you start the engine. Otherwise, it can stay in the open position even when you pull the control cable.
Idle mixture, idle speed, and fast-idle speed must be adjusted properly. See this
link (click here for the OEM repair manual) for how to do these adjustments on an Aisan 16030 carburetor, as well as other adjustments.
Number of turns for the idle mixture is a coarse adjustment. Idle mixture should be adjusted with a tachometer on a running engine using the lean-drop method. See the link above.
Small local carburetor shops usually collect carburetors from junk yards and rebuild them. If you still cannot figure out what's going on, you can go to one of these places. I am guessing some incorrect adjustment, incorrectly installed or broken part, or some vacuum leak. A hot engine shouldn't stall even around 600 RPM. So, there is something wrong but it's no rocket science.