i think this may be electrical

I have a 2 wheel drive, automatic 2003 Chevy Cavalier (96400 mi.) that seems to have a problem.......first when i get in my car and close the door and put on my seat belt, the overhead light is supposed to turn off but lately it does not, until pull out of whereever i am and put the car in drive......it will also come on periodically esp at stoplights.......THEN whenever i park the car the alarm will sound off by itself after about 5-10 min after it having been parked.......what in the world is going on here??