No...you can buy a rechargeable 12 v battery for about $15
No, it only cone with one that suction cups to your boat. I think you can buy the ice transducer separately.
sorry, I do not know about ice fishing; we live in Florida -----no ice ! The Humminbird works fine in Florida waters.
CS3 12 volt 7.2 amps per hourThese battery is recharchable