Vehicle stalls on forward and reverse gear, what would cause the stalling?

It sounds like the torque converter is locked up, when you put it in gear does it act like a manual transmission car when you let the clutch out too fast? Can you please shoot a quick video with your phone so I can see the car go into gear? That way I can tell for sure what's going on.

When you put it in gear does it act like a manual transmission car when you let the clutch out too fast? No.
When you put it on forward gear(drive) it will take off normally but hence you throttle it to move faster, it will move and immediately you remove your leg from throttle pedal to depress brake pedal, it will off. It does this on forward and reverse gear, if you gently press the throttle, it will not go off and if you enter highway, it runs fine and shift properly.

okay, then it sounds like a vacuum leak, or the IAC valve needs to be serviced. here are to guides to help you, make sure the engine is cold before you do the vacuum leak test:

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

This is a generis guide to help you see how to do the job with diagrams below for your car:

https://www.2carpros.com/articles/idle-air-control-valve-service

Check out the diagrams (below). Please let us know what you find.

Okay, then it sounds like a vacuum leak. Please send me a clear picture of vacuum diagram for me to check if the vacuum hoses were properly routed including EGR and EVAP VSV.
For the IAC, I replaced throttle body when I noticed that the previous IAC Revs higher at idle and when you disconnect the IAC connector and it drops to normal. So let me check vacuum lines first. Thanks

Here are the vacuum line diagrams AllData offers in the images below.

I did not understand the routing of this diagram, I have all data, but I am not understanding it that's why I ask for picture not line-diagram.

This is what we have, I am not sure where to get an actual picture. Sorry we couldn't have been more help.

I have checked and noticed that EGR vacuum switching valve and pressure up vacuum switching valve are broken and there was no hose to them and I replaced them and routed the hoses to them. Then the higher idling at 3000rpm drops to 1,400 RPMs, then I loosen the stop-screw and the throttle plate fully close and the rpm drops to normal at 1000rpm and if you engage gear, it drops to 750rpm. I test-drive it and it didn't stall again only that sometimes on reverse if you throttle it, it will move backward and if you remove your leg from throttle pedal as to hold brake pedal, it will jerk as if it will stall and at this time the rpm drops below 750 and it will come to normal again. But on forward(drive)gear, you will not notice anything unlike before when the vacuum are bad.