Have you checked the key fob battery, as these can affect the alarm going off, if there's a partial implausable signal from the remote when you press the button. Change the remote battery as matter of course too!
the horn is prolly earthing though a bracket, would take it off and give the point it connects to the car a good clean and the point the horn connects to the bracket just to make sure its not a earthing fault, if still no joy check to see if your getting 12v to the horn