ELECTRICAL ISSUES

What is your question?

My 99 isuzu rodeo is doing weird electrical things. The alarm goes off when no one is near it. The dome lights will stay on even when car is off and key is removed from ignition. Also, now when I take the key out of ignition sometimes the heat or stereo will turn on by itself. This happens randomly even through the night when no one is messing with it. It's gotten to the point it keeps decharging my battery now? Does anyone know what might be causing this?