I get the same issue on the gas gauge. I've replaced a leaking capacitor in my cluster, and the problem lessened. It was at a point where the tank would show empty erratically when I got to half or less. The thing's still not quite accurate though I might add. Not a big deal for me since I like to fill her up before it gets on empty. Less money at a time.

As far as your engine cutting out, it sounds like the fusible link is the problem. You'll see a good description of its associated problems on bmwe34.net, a great reference. An easy fix.