i personaly would say it's a window regulator as the lights are dimming showing a drop in amps, so the window in theory is trying to go down (or up) but isnt, to be doubly sure you could try search for the wiring diagrams on google or a bmw forum to check the wiring, i assume it's a bmw as you mentioned it, and i dont think its that uncommon for a regualtor to fail to be honest, dunno about the fuel gauge, could be a fault with the sender inside the tank, i work for land rover and the freelander 2's have a slight issue on some where a pipe or cable tie on the sender catches on the float so cant go the full travel, check and make sure it's got a good earth as well that can cause you problems aswel
jope that helps mate