Seems like quite a few random things going on there. My first thought would be a major short circuit or malfunction, possibly somewhere in the driver's side dash or near the fusebox in the engine bay. It's not unusual for wires to get frayed or melt. But that's just an uneducated guess at this point. There are quite a few 5 series owners here that may be able to lend some better expertise, so stick around and see what responses are generated
You didn't mention where you're from; maybe another member here is close by enough to recommend a reputable shop. Beyond that, can you locate another BMW dealership in your state that can properly diagnose these issues? It seems these problems require such specific experience, and that may be your best option.