1. A shunt controller probably means it regulates the panel's output by shorting the extra power to ground.
2. Probably.
3. A "capacitor" doesn't have these problems, but the storage battery does. Deeply discharging a rechargeable battery damages it, so you want to just shut off the device when the battery voltage drops too much. Overcharging a battery which is already fully charged can be bad, depending on how high the charging current is and the type of rechargeable battery in question.
4. Yes. The exact meaning depends on context though.