If you lock the car, it will randomly decide that the alarm should go off. If you prevent the car from automatically locking, you can prevent the alarm from being armed. However, the other problem which I think is related is that there are times when the car will simply not start. If you go back later, it does start and is then fine for a while, sometimes weeks.
I think it might a problem in the factory alarm that thinks you are trying to steal it. It would seem like there must be a way to disarm it. If you were going to add an after market alarm system, wouldn't you have to disarm the factory alarm?
I would like to disable the alarm system and see if that clears the problem. Plus I could start locking the car again.