A New Used Car, help diagnose

[JediBrain]

Greetings,

I recently acquired a used '87 325e, and as I drive it more and more and listen to it, I am noticing a few things that cause me some concern.
To preface, I have researched all these problems individually, and present them here all together in case some people see correlations between some problems which may save me time and money. Any and all guidance is welcome; the more information I have the better I will learn and solve my automotive woes.
Since I got the car, here is what I've replaced: oil, oil filter, air filter, fuel transfer pump (in-tank). I've also used fuel injection cleaner gas treatment.
After I've been driving around a bit and the engine is at normal operating temperature, when I come to a stop I will see the needle on the temperature gauge begin slowly climbing. When I was stuck in a traffic jam a few days ago and sat for several minutes going nowhere, I watched the needle climb to just under the red zone. Once I get back underway, the needle will fall back down to the nominal range.
The coolant warning light will go on after a bit of driving, sometimes short, sometimes long. Every time I check the level (when the engine is cool enough to do so) it is fine. I will ignore it and the next time I start it up the warning light won't be on, but will sometimes come back on after a bit.
My odometer sticks. Sometimes it will unstick itself, but then will get stuck again. Resetting it doesn't fix it. This is an on-again-off-again problem. A tap on the instrument panel screen can encourage it to start rolling, but success with this method is infrequent.
When I have my brights on and switch them off, my low beams on the main headlights will sometimes go out also. Switching the brights back on will turn all 4 lights back on, and switching back will sometimes correct the problem. Flashing the brights will after a few tries get the mains to stay on.
My external fuel pump is loudly buzzing. It had been very loud, which led me to discover the fuel transfer pump was dead. I swapped it out, but the buzzing persists, though at a lower volume. Does this necessarily mean that it is near death and needs to be replaced, or could something else be affecting it?
When I'm driving and take my foot off the gas to coast, sometimes I will hear a knocking sound coming from the rear passenger-side. I researched this and the posts I read said it could be the catalytic converter bumping up against the heat shield. I inspected the converter and it was solidly in place, and don't see any other part under the frame it could be knocking up against.
When I turn the engine off, the battery light will come on and fade out. I cleaned the battery terminals, but it still comes on. Is there a specific point I should be looking for where the battery is discharging, or would I be better off looking for a needle in a haystack?

If you can elucidate any of these woes and help me alleviate them, I would greatly appreciate it. If you live in the Santa Cruz area and are a proficient BMW mechanic, I will trade my homebrewed beer for your teachings. :-)

-Nick

[Bear]

Lets solve the near overheating first. Generally if she overheats at idle or in traffic but not at speed then the viscous fan clutch (a mouthful I know) needs to be replaced. The clutch is that aluminum casting on the front of the fan (the fan attached to water pump). This device is replaceable and remeber to remove it is left hand threaded (turn clockwise to loosen). The trick is to hold the pully from rotating while unbolting the clutch(32 MM nut if my memory is good0. A tool is made to do the job, but anything that will keep the pulley from rototing while you whack the wrench on that big nut will work. From there it is straight forward.

[drhyde]

i agree with bear normaly the viscos is the fault with the overheating. with regards to the lights i have had this problem before and it was the headlight stalk that was faulty. the odometer on the e30's the gears on the actual gauge get brittle and wear this could be your problem. the knock maybe check the diff bushes.