[jmillet]

If you want to go with Red Line fluids then it's MTL not MT-90 for the transmission and either 75W-140 or 80W-140 for the differential.
My Z4MC lives in a mild climate (Seattle) and sees many track miles so I use a 50/50 blend of Red Line MTL and MT-90 in my transmission and 80W-140 for my differential.
I second RobertRO's advice; drive the car awhile before trying any major maintenance tasks like a valve adjustment. While not brain surgery it is a tedious job that demands attention to detail and patience.