Skip the Dawn wash. There's no need for it, especially when polishing. It's also not absolutely necessary to wash after FP. There are no oils or fillers left by FP.
You can buy the PC from Lowes and buy a backing plate plus pads, or you can get it from somewhere like Coastal Tool and it will come with a backing plate.
The most important thing you are leaving out is TOWELS. These are going to help keep your finish swirl and marr free. I suggest
www.pakshak.com and
www.exceldetail.com
Don't be afraid to crank the PC up to 6 if your car needs it. It will make you job go much quicker. I suggest having several white pads around. You'll find that you use them more often/frequently.
Here is a very helpful article:
http://www.bettercarcare.com/articles.php?articleId=47