12 Codes 313,300,444,305,303,306,302,301,304,174,171 does anyone know what the issues are? also My car shakes & shuts off if I'm at a complete stop for too long but drives fine on highways.

run fault codes to find the faulty cylinders. With the fault codes You can get a list of possible things that can be checked and replaced.

Any codes?

sound like you have a cylinder not firing properly, a tune-up would be the first thing i'd try

The AC solenoid isn't working. When you turn on the AC this solenoid on the throttle will kick the idle up a little to keep it from stalling when you let off the pedal.

you may have a fuel filter/pump problem which can cause this type of problem if it can supply enough fuel to run the motor,and can cause stalling problems and popping noise out the exhaust.you may have to have it put on a scan tool to check for a code that may not set the check engine light,and the car driven with the tool on it so they can take a snap shot of the problem when it happens so they can study the information to see if something is showing up.

First thing I would do is make use of Autozone's(or similar part stores) free engine diagnosis. They can print you off what codes your vehicle is throwing and let you know the most likely causes and fixes for your issue(s).

First you stop driving a vehicle with those issues.

The shaking could be several things. The EGR Valve,if some slamming and banging,type symptoms,especially going up hills.

Loss of power could be the TPS Sensor and a bad COP Ignition Coil.

Very loud --What?

High RPM ,as you already know ,could be the trans slipping. Another in a long list of LS issues. That would be a bad Trans Solenoid Pack.

I have a 2004 LS and had all of them,happen.

You need to pull codes,before you start to troubleshoot thoses items.
I would imagine your driving around with the MIL Light ,light on the dash?

Get codes,give them to me, I'll help you out. Do not drive it, untill it is properly repaired. The LS is a very,very complicated high tech vehicle.

Many things can cause it But A Bad IAC Motor (idle air control motor) can cause stalling and shaking to a point when you stop if its not providing the proper air mixture .

its possible that the idle stepper motor is having problems or there may be a leak in the vaccum lines possibly check the main one going to the brake booster