i'd really suggest you go read through some of the popular worklogs on here. that will answer a lot of these basic questions and give you plenty of more complicated ones to start pondering as well.
1) you will need a DC power supply to convert 12v to whatever voltage your laptop requires. you will most likely end up wanting an intelligent PSU with an integrated startup/shutdown controller - check the "Store" on here for some options.
2) certainly you can run a 3.5mm stereo to RCA cable from the laptop's line out to an aftermarket amp. you may need a ground loop isolator if you get noise. if you have a factory amp that only takes speaker-level inputs then you will probably need a line-driver, though i guess you might be able to run from the headphone output of the laptop if it's loud enough. something like a JL Audio CL-RLC might be useful as it will isolate noise due to it's differential inputs, can act as a line driver, and gives you a physical volume knob.