I would not necessarily trust that your English teacher is knowledgeable of laws regarding discharge of a weapon, particularly when the intent is to maim or kill. In most cities/towns discharging a weapon except to protect life is illegal--it is too easy for a stray bullet to injure or kill an innocent bystander. But it really depends on your state and local laws.
Of course I would be angry if someone did something to my animals, but the proper response is a legal response, not escalation into a blood feud. I suggest that you or your parents verify the noise and nuisance codes for where you live to make sure that you are not in violation. If you are in the clear, you should report anonymous notes and threats to the police or sheriff. If you are not in the clear, you need to do something to prevent the neighbor who dropped off the note from going through legal process to have you fined or your dogs confiscated.