Yes, unit comes with a power supply (decent length too). So you have the option of battery power (portable) or plugged in. FYI if you use on bettery power, remove batteries when not in use. It will continue to drain batteries when powered off. -Cheers.
Yes. You can power from the supplied 110 V AC power supply or 8 c cells. Also, if you check around you can find a 12V DC power converter so that you can plug into car power outlet and power connector at the back of the unit.
Yes the unit comes with a power cord and power supply. It has a decent length to the cord. It also uses "C" batteries. They do not seem to last long, although I was not aware that the batteries can be drained when it is powered it off. I do like that I can use the unit indoors with it. I hope this answeres your question.