When I went (3 days in June), I saw a lot of Suzuki Swifts, Renault Megans, and VW Sciroccos from the car rental outfits in the area.
The times that you picked are ok, but if you can stretch it out to 9/14, you'd have a much better chance for an "open" lap. If there's an accident and the track closes, you're out of luck!
As for traffic, the answer depends on what you are comfortable with. I did it in my ED M3 (before 1200-mile service!) and I had never driven a track before, so I wasn't comfortable with a lot of cars zooming past me. From that perspective, you want an earlier time (When I went at 8 am, there were only 7 cars on the track).
Your driver's license should suffice, Germany allows you do drive with a US license for 90 days.
Finally, no helmet is needed. I'm not even sure I would recommend one, given the possibility of the red mist!