The symptoms that you are describing, the horn like noise, the erratic idle and stalling, all point to a problem with the IAC.
Whenever you replace anything on top of the engine (sensors, IAC, etc.) you need to disconnect the battery for about 20 minutes so that the computer can clear out it's memory. After re-connecting the battery, let the car idle for about 15 minutes so that it can relearn its new idle parameters after the new parts are installed.
Re-check everything that you did on the car and make sure that all of the electrical connections and vacuum lines are installed correctly and everything is tight.
DO THE IDLE RELEARN!
Also, I'm not a fan of aftermarket CAI's. Although, they typically don't make a "fog horn" sound. They don't add any power to the engine either. If its installed correctly, it shouldn't be making the noise that you are describing.
The stock air boxes are generally pretty good performance wise, so it's your call...
Just out of curiosity, what brand of IAC valve did you buy?