2001 Altima alarm goes off for no reason and my doors keep coming unlocked

For the past two weeks when I get into my car and lock the doors they come unlocked while i'm driving. In the morning my doors are unlocked when I know I locked them the night before. I have not been using my remote starter. I have been locking the doors manualy. For the past 4 days my car alarm goes off for no reason. I push the button on my remote starter and the alarm does not respond immediately. The alarm just goes off with no manipulation, while I'm driving or in the middle of the night. What should I do? I thought maybe it was the battery in my remote starter, but I took the battery out and the alarm still acted crazy. Should I unhook something like the horn until I can get it looked at? What do you suggest? thanks