Is this and intemittant problem or all of the time ??
I think we are dealing with more than 1 problem here . The fuel level sensors on bmw vehicles are not the best and tend to go out , so it would be a good assumption that you have a bad fuel level sensor or both have gone bad . It would not be uncommon to replace both , at the dealer level we can check the control unit for faults . The speed sensor is in the differential . The brake light switches in you car are also known for having problems , most of the time its the part of the switch for the check control your car being a 318 may or may not have the check control .
Both the speed sensor and the fuel level sensors share the same ground splice .
I would remove the trim panel around the brake and gas pedals and inspect the wires for any issues such as broken wires . The ground splice for the fuel and speed sensors is also in that area , the wire diagram does not give an exact location of the splice so i cant tell you exactly where its at .
let me know what you find .
BMW Technician
12 YEAR MASTER TECH