The alarm is buggin out, it is the one that came with the car from the factory. When you use the keyless entery button, it likes to set the car alarm and the little red light flashes.Also having a promblem with the wireless key, the unlock and lock button stopped working the only things it does when, youpush the lock button it sets the alarm. and the same thing with the unlock.
Open the inside of the key fob. There are some carbon circular discs on the other side of the rubber button. The carbon discs contact the circuit board when you press the button and in turn send a signal to the car to lock/unlock. That sounds like your problem regarding the fob not working (unless it ain't the battery). About the car setting the alarm off when you use the fob. i can offer no suggestions but i will say that although it may be quite expensive to have the system checked i think it would be worth doing rather than buying a new alarm because the original alarm is of very good standard. Hope this helps