Don't overthink it you should have a book with your car that details the standard service intervals (15,000 miles / 2 Years) along with all of the things that need to be checked. The general consensus on the internet is that those intervals are a little too long so most people do an annual service/oil change which in my case works out also to be about 6k miles.
See these two threads for info on what is checked, if you look in your service book you should see a similar checklist.
https://www.bimmerfest.com/threads/z4-e46-service-maintenance-checklist-2006.171200/
https://z4-forum.com/forum/viewtopic.php?t=98676
With regards to doing intermediate oil changes between inspections there are some people who say don't reset the service indicator so that it flashes up and tells you when Inspection I and Inspection II are due, if you reset the service counter each oil change you will get out of sync this is the BMW way.
Or you can do as I do and just keep a log on the paperwork and do Oil Service, Inspection I, Oil Service, Inspection II and start again on the cycle. I missed a brake fluid change doing it this way because my service counter got all out of sync and I didn't check my notes before taking it in for its service/MOT pamper session.
Brake Fluid Flush every 2 years
Gear and Diff oil every 50,000 - 100,000 miles (Supposed to be lifetime)
