engine immobilizer & keyless entry system???

[person1]

Hi,

I live in Fort Lauderdale. I just bought an Automatic 2006 Corolla CE with Power Windows, Door Locks, Keyless Entry, Carpet Mats, and a full tank of gas for $15,000 OTD (including tax, transferred tag, and title)

1. I know that Corolla CE has an engine immobilizer. Am I correct that no one can start the car unless he has the key with the right transponder?
2. The dealer installed a Keyless Entry System (the brand is Automate, the model is AM 2). Am I correct that the keyless entry system will deactivate the starter once I press the LOCK button? And even if someone can get into the car they cannot start the car
3. I always use the Club to lock my steering wheel
4. I was thinking to have an alarm system installed

My questions:

I. Do we consider Keyless Entry System as an alarm system (or as effective as an alarm system)?
II. Are the Engine Immobilizer, Keyless Entry, and the Club safe enough? I wonder if installing
another alarm system in the Corolla is just too much.
III. Did I overpay for the Corolla?

I am myself not familiar with auto security system & thank you for any feedback.

Person1