Can I hook up up a 820 watt amp to a 96 cavalier without causing damage to the battery or alternator ?

The specific you're missing in this question is the brand of amp. The subs have little to do with what will happen electrically. Amp size really won't effect anything in your vehicle unless the car is off, or you listen to hard hitting bass at high volumes. Then you'll get headlight dimming as well as interior light dimming when the bass hits. This is due to large load requested by the amp, that your car's electrical system is up to. You might want to look into a capacitor (hold electrical charge when needed by car stereos) or re-winding your alternator at a stereo shop to supply higher amperage.

Yeah you can. Just make sure that you have a good ground and no bare wires.

sounds like a good setup. I have a 99 cavalier, I set a switch for the amp which reduces the need for a constant power supply, I kill the amp when I do not want it.

It should be fine, just dont run the audio system for long when the car is off.

If you really know what you are doing, it should be fine, but your hearing is much more important!

Yes that should be fine i have 2 12 1000 eclipse with 2 amps in a Grand Prix and with a good battery and alternator this runs just fine. Turn it up and have the car running and watch the lights if they really start to dim down then i would suggest getting a Clarion Deep Cycle battery they are around 150 but it is worth it to make sure you don't blow out any eletrical. Other then that you should be good in that small of a car. Hope It Hits Hard for You

yeah your straight, i have a 800 watt rms fosgate mono amp and then a 200 watt 4 channel for my speakers through a distubution block on stock alt and a die hard battery.