1993 325i questions - mostly electrical

I have a 93 325i with 160k on it, aside from the ever deteriorating head gasket, it runs like a top.... normally. I have a few questions i was wondering anyone might have some pointers about:

A rattling noise: In my right rear. Only when I hit potholes or otherwise rough road. Replaced the rear shocks and mounts, and checked the exhaust thoroughly. Still no luck.

Dim instrument panel: But only in the digital readout where it shows the overall mileage and especially the per tank mileage counter. Is this a tough fix?

Dying battery: Car runs fine on my 27 mile jaunt to work in the AM, but starts dying halfway thru the pm commute (ABS light flickers, headlights dim, stereo cuts out) I _had_ been pulling into a parking lot, turning the car off for 4-5minutes, whereupon it'd start back up good as new. But the other night it pulled the same thing, but died completely. If this were the alternator, wouldn't it just crap out altogether rather than slowly regaining charge? Brand new battery, clean terminals. I have noticed that something(sounds like a little microchip cooler fan almost) in my dash or engine runs about 10minutes after I shut my car off, but it didn't do this to my old battery the previous 2 years I owned the car.

Towing eyebolt: Anyone know where I can find one without buying the whole emergency kit?


Help would rule! Thanks.

you could check the alternator.... with the car running put a volt meter across the battery.. it should read 13 1/2 volts if the alternator is working... if you don't have a volt meter, just disconnect one side of the battery, if the car stays running then the alt. is good ...