You don't need to wash the car between each prodcut application. It also is not necessary in all cases to use multiple passes with the same product like #80 2x. While I might not have emphasized it as strongly as Mike did, I did mention picking a test spot on your car to apply your process to and make sure you get the results your looking for before doing the entire car.
I did exactly what Mike wrote and took a test area on my hood to see what would remove the swirl marks and scratches in my paint. After going over the test area with one pass of #80 there were still some scratches and swirl marks in the test area. It had definately reduced them but did not eliminate all of them. I choose to try another pass of #80 in that area and start another test area next to it and do one pass of #83 to see which one would work best. After completing both test spots the car was pulled back into the sun for inspection. What I found was the 2 passes of #80 looked better to me than one pass of #83. So, after going through this exercise I made the choice to use 2 passes of #80, which was going to take longer, but the results would be better than doing one pass with #83. Now that I knew what was going to give me the results I wanted I could continue and complete the entire car. I already made the decision to use #7 and 2 coats of #26 but I really should have tested both of those before doing the entire car to see the final result before applying them to the whole car. This was my personal car and while I might have spent time applying #7 with no additional benefit because I didn't test it first it was what I wanted to do which is why I didn't bother testing that even though it should have been.
Claying the car should remove the current wax from it but don't EVER use detergent soap or dish liquid on your car. There are much better things to use. A good car wash soap is all I ever use on my other cars and I always use the 2 bucket method to reduce scratching the paint, even in my daily driver vehicles.
I know it seems overwhelming at first and you want to do everything right and with some time and patience you will find the answer to all your questions here. Check out some of the other threads for more information.
If you have never used a DA polisher before I might suggest trying it out on some of the other cars you may have. I did that with my 2 daily drivers just to get better aquainted with the amount of pressure to apply, trying different products to see their result and going through the process so when I was ready to do it on a car a cared a little more about I had increased my confidence level.
I just finished my Z and it came out great! There are no swirl marks in it when inspected in full sun. I need to get some pics so I can post in a seperate thread here but its looking very nice. I also went to a club event this past weekend and several people commented and noticed how shiny my car looked when I pulled up. That's always a great feeling when others comment on your hard work!