1996 E320 - about a week ago, the odometer and tripmeter LED's got dim, but not the outside temp or clock LED's. Today, the fuel gauge stopped working. Are they related? Are they fixable at home?

 

They don't sound related. You can pull the cluster and check the lights in the back to make sure they are making contact if it is a backlighting issue. The fuel gauge could be the sending unit in the tank not working. I would pick up another cluster off of ebay or at a salvage yard and swap it out to see if the problem is present on a different cluster.