BMW Questions? Ask a BMW Repair Expert for Answers.
At first glance it seems that those two problems are seperate. The dynamic drive warning can be on for several reasons from low fluid level (You mentioned you already checked the level, Did you do it with the engine running?), the other reasons can be from a failed sensor or control unit. To determine it you will need to have the vehicle scanned by a BMW diagnostic computer to read out the faults.
The radio cutting out could be any module on the MOST (a fiber optic entertainment system communication bus) to a faulty module, radio or amp.
With all of that being said low battery voltage can wreck havoc on modern BMWs. If you are suspecting the battery being low I would recommend replacing it. Not only is it good maintenance it can prevent a break down for you.