Okay in answer to your questions:
1.) Whether or not your standard battery will cope depends on what else you are running and how loud/often you have your system cranked up. To give you an idea I am running 3 amps, 2 x 12" subs, 5.6" screen, playstation and a few other bits (speed detector etc) and I have no problems with mine. So I reckon you should be alright.
2.) Invertor - go to an ICE specialist. My local Ice dealer wants 170 quid for the ps2 invertor which he reckons is a special type of power supply. How true this is I dont know. The invertor for the playstation 1 is only 80 quid though. I bought my invertor off ebay for 44 quid. (Sorry for all the use of the word quid but the pound symbol is broken on my keyboard!)There are a couple of companies on ebay that sell them with different wattage ratings. Have a look on there you will definately save money.