You're better off posting in the e90 section since this section is mainly for M3's.
Failing batteries can cause a host of issues and tons of fault codes. If you suspect it might be the battery, measure voltage with the car on and with the car off. With it on you should see 13.8 to 14.3. With the car off you should see 12.2-12.7.
If there is no issue there then proceed with diagnosis of what would cause those faults.