What an odd combination of symptoms! Very difficult to reconcile, and what they have to do with the humming noise ... hmmm ...
When I hear about weird electrical problems that make no sense, what I've gleaned over the years from this and other MB lists:
1. Often OVP (overvoltage protection) relays are at fault. I'm pretty sure your car doesn't have an OVP (since it's basically the same as my car and I don't have one.)
2. Fuses, though looking good, can actually have hairline cracks and cause all sorts of weird, intermittant, nonsensical electrical glitches. One MB guru recommends replacing all ceramic fuses every ten years. You might want to go ahead and replace all the fuses even though it's a year early.(Get fuses from dealer -- I just did mine.)
3. The other thing that can cause weird electrical problems is a bad ground somewhere. Do you have the repair CDs? They have a listing of all the grounds. Even if you don't have it, you might want to check out the obvious grounds you see under the hood (e.g., near the right-side front shock tower) and in the trunk, near the antenna. You might get lucky and find that cleaning and tightening a bad ground connection could solve your problems.
If all else fails, and you can drive it up here, I have a GREAT independent mechanic who charges $55/hr and would track down your problem pretty quickly, I'd bet.