It's probably your battery since you didn't register it. You can check on realoem to find the price of the alternator. Mine was replaced under warranty, but I was thinking the parts cost was around $700.
Here is a video I took when my car started going crazy. I was on the highway 150 miles from home. I got some of the same messages as you along with the steering wheel being hard to turn. Pay close attention to the speedometer as well. Pretty scary going 80 mph and having this happen.
Edited the terrible curse words out of the video.
2008 E63 M6
- Black Sapphire - Sepang Bronze Full Merino - Carbon Fiber Trim - Alcantera Headliner - SMG - HUD - Soft Close Doors - Comfort Access - Individual Audio w/Sat and HD Radio
2009 E92 335i
- Black Sapphire - Black Dakota - Burl Walnut - Sport - Premium - Cold Weather - Navigation - L7 - Comfort Access - Smoker's Package
Member: BMWCCA #471614