Hi! The fuse for seat without memory is in the engine bay, next to the engine ecu, the car's right side. The fuse number is 15. You can try to change your instrument cluster with an E38 or E39 cluster to see if it changes.
You can find a DIY here: http://bmwcoders.com/forum/bmw-gt1-ops- ... matic-839/
or you can buy it here: http://www.ebay.com/itm/BMW-INPA-Ediaba ... 1115011595
The Inpa is not too difficult to get, if you have the interface, just PM me.
Hi! It can be the Abs modul, especially if it's number end is 001. Solder problems can cause this if it stopps to work when it's hot. I would change it for a try.
You have to register the battery change in E60/E61 with diagnostic, if don't, it can cause battery charging problems. You should check if the registry is correct in the car. (sorry for english)