The cables you're looking for might pop up on ebay...if you could get pics of the connections we might be able to tell you if you can find a universal cable to fit the specific plug.
It can be hooked up in the home, you would need a power supply that puts out about ten amperes. My opinion about said procedure: it works great, but the only problem is car headunits are made to run a few hours at a time...so heat becomes excessive. This in turn could cause damage to the headunit if it is not left enough time to adequately cool down...
Installation in the car might be difficult because you have to find a place for each component of the headunit/system and run all of the new wires; most of the time, all you replace is the headunit itself and all of the wires needed are present.
In my opinion, installation in your car would be the best option, however if you don't mind keeping the unit cooled down (turning it off after 2-3 hours), it would sound great in your home...