What is the difference between fuel control unit and fuel flow meter (transmitter)?
The Fuel Control Unit controls the flow of fuel to a turbine, it is in effect the mechanism by which the throttle works. 

A fuel flow meter is simply a device that measures fluid flow (in this case the flow of fuel) through a line. The location, quantity and operation of flow meters varies by aircraft and configuration. Broadly speaking they are used to calculate actual fuel burn as well as to make sure the proper amount of fuel is flowing to an engine. 

The fuel pump is the device that drives fuel to the engine/FCU from the tank. Again systems vary heavily but broadly pumps are used to move fuel from the lowest point in the tanks to an engine that may be above that point as well as to build sufficient fuel pressure to allow injectors/delivery systems to work. 

In the simplest of systems a fuel pump sends fuel over a fuel line to an FCU. Somewhere on that line is a flow meter so that you can measure fuel flow out of the tank, into the engine.