From what I can tell, this K56 relay disconnects the battery from the alternator to prevent a fire, in the event of a crash. Usually, it seems that an airbag deployment would be necessary to trigger the K56 to blow and once it's done, it can't be repaired. As the car ages, other things such as moisture, might trigger the (airbag sensor or fuse?) to send a signal to the K56 to blow, or it just goes out on it's own eventually. It's a little confusing to me right now.
The K56 was only used on the very early R170 cars (1996-mid 1998) and after that, it was replaced with a different set up, some kind of pre fuse system. The big problem with the K56 is that, if it blows, you don't know it, until your battery light goes on. You then have however long it takes before the battery gets drained and the car dies. I shudder to think of all the places I have been with this car and somehow that didn't happen.
If you place the generator wire from the G post on the K56, to the Battery post, or jump the two posts with a copper wire, it is supposed to restore all the electrics and the generator (alternator) charges the battery again. It seems like this has worked for everyone on the internet with this problem so far, except myself. Hence why I am suspecting a low quality voltage regulator as the culprit, or perhaps that is wishful thinking and the alternator it's self just died as well, or the alternator wire harness. After I replaced the voltage regulator (and connected all wires to the Battery post), electricity was restored, the battery light was off and the car worked for about 40 mins before the battery light came on again.
As for needing to reset systems after a battery change, I'm assuming that this car is no exception, though I have changed the battery or disconnected it often in the past and I've only needed to reset the radio.