1. I have never seen one
2. Absolutely, if your car supports it is another issue, but that amount of power will have to hard wired in directly to the battery terminals.
3. That would be dependent on the alternator output, and the draw of your car. IF yo do some research on highend car audio systems many vehicles will be outfitted with multiple alternators to provide the power needed.
Sounds like an ambitious project but I do not know why you would need a 1kW PSU, the only systems that need those are usually the SLI multiple 200+ watt video card systems. I first thought maybe you were going with a server type system but most of those would use a dual PSU setup for each physical CPU
Perhaps a little more info on your research project and we can provide more help for you.