03 GM Alarm Issue
 

I have, what some might consider, an "interesting" car alarm system. I purchased the vehicle used - with one owner, and an original factory "anti-theft system" that has an alarm. Whenever I am going to leave my car for an extended period of time I'll hit the "Lock" button on my key FOB and walk away. Now, I have a few questions I would like to pose and I believe this is a great way to start -

After pressing the "Lock" button on my Key FOB, I hear two beeps (and also see the lights on the vehicle flash) ... but then, a delayed third beep. The time delay for this third beep to happen varies wildly - but I have narrowed it down to between two to three seconds after the initial two horn and light chirps go off. Is this normal?

As for my second question:

One day I went outside to place something back in the glove box of my Grand Marquis. Since I know the door code for the keypad I went ahead and started to press the first number and immediately the alarm started to sound. Is that supposed to happen?

Lastly:

I have reason to believe that my "factory anti-theft" system has been modified. I have two LED indicators: One to the left of my steering wheel towards the driver's side door; and another on the dashboard. Are there supposed to be two?

I know that these may sound like "stupid" or "amateur" questions, however I am truly puzzled as to why my alarm is functioning the way it is. I have been dying to use my keypad for the keyless entry system, however the alarm is getting in the way of this.

Any help in these matters would be truly appreciated.