The alarm keeps going off when the car is.

Short is just removing the system, all you can really do it put it in valet mode so it doesn't arm. That would only be a temporary "band aid" approach though. I would have the system either removed or replaced unless you can find what is triggering it.

I'm assuming this is an aftermarket alarm system that has been installed. All of those system have a mode it can be put into that prevents it from arming that is commonly used when you "valet" park your car. There is usually a small switch or button that is activated when the key is on and that suspends arming of the alarm.

I guess that depends on whether it's a horn going off or a siren. It would have to be a horn to be factory and if that is the case, someone is going to have to determine which trigger is causing it.