uhh live rock is SW & this is general FW. im sure you'd get more responses if you posted this thread there
Live rock does have stuff growing on it and thats what makes it live. but no its not live in the sense that it grows. and im not sure it will do ok in cold water. and i know that its fairly expensive and is priced by the pound.
You can put coldwater liverock in cold water, but dropping tropical liverock in cold water will be bad.
No, it doesn't grow.
It's expensive, at around 5 bucks a pound.
It's for saltwater only, which I assume you already knew, but just in case...