Car PC integration with Android phone for Hands Free calling and more?

I have a Galaxy S3 and a high end, but beat to hell laptop. The laptop wouldn't fetch any money on eBay due to the overall condition. But the internals are pretty high-end and work great. So I'd like to turn it into my first Car PC.

But how do I get hands-free calling working between the Car PC and my Android phone? I don't want to have any cables between my phone and the car PC.

And is there any software that will let me mirror my Android phone onto the Car PC so I can control my Android phone via the touch screen 7" monitor I'll be using?

I want to totally get rid of my car stereo and use the Car PC for all my audio needs.