Idle goes down and shuts off when A/C is turned on and when transmission is shifted into gear

Welcome to 2CarPros.

When a load is placed on the engine such as the ac, there is what is called a stepper motor or idle air control (IAC) motor that is to adjust for the load to prevent issues. If that doesn't respond, the added load can cause the engine to stall.

https://www.2carpros.com/articles/how-to-replace-an-idle-speed-control-motor-iac

Also, have you checked to make sure there are no engine vacuum leaks? That can cause a rough idle and stalling as well.

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

You mentioned the intake air control valve. Did you mean the idle air control valve? If so, did you check to see if there was any dirt, carbon or corrosion in the throttle body where it mounts?

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

One last thing. Have you checked the throttle body to make sure there isn't a build up of carbon or dirt in it?

https://www.2carpros.com/articles/throttle-actuator-service

Let me know if anything here helps or if you have other questions.

Take care,
Joe