The beeping probably comes from your converter/charger or inverter/charger (which ever you have) or from something that requires 12v power (propane detector or maybe the fridge). It is likely a low voltage alarm of some sort. I know our inverter will beep if the voltage goes low when it is on, though that would not happen on shore power, and our Norcold fridge beeps if it loses 12v power.
As Ned says, your first chore is to find out why the batteries aren't being charged. A shorted battery will usually cause the charger to shut down. Your interior lighting is almost all 12v, so it is powered through the batteries and charging system, not direct from shore power. Have you checked the water level in the batteries (I'm guessing they are the flooded cell type)?