The dishwashing soap has a degreaser in it. A popular brand name here in the states is "Dawn" Dish soap. We use that to get a lot of the old wax and stuff off the car. It makes the surface "squeaky clean"! Don't wash your car in the sun if it's really hot out. The water dries on the paint too fast (especially on dark cars) and leaves spots on it. Dry the car with a lint free towel or shammie. That will leave the paint really clear of hard water marks and such. You can use a clay bar, that you can get at better auto parts stores in the U.S., but it's a lot of work.
I never wax my car in the sun, even if the mfg. says it's ok. The shade gives you more time to get it off, in case something takes you away from it for a few minutes. I use Meguiars Tech wax and am very happy with it. My car is white, though and I don't think flaws show up on it like it would on your Red one. I think the RED is awesome when it's clean and polished! Good luck!!