FADEC is Full Authority Digital Engine Control, it calculates, controls and monitors functions of a turbine engine. Most FADEC engines have only an electronic interface with the aircraft though developmental stage engines had partial mechanical control.
FCU, I believe GE's acronym for Fuel Control Unit A hydro mechanical device later called a FMU I believe or Fuel Metering Unit which is electric hydraulic. The FMU works in conjunction with FADEC.
HM, the only thing that comes to mind is a HMU or Hydro Metering Unit, a Pratt term for their electro hydraulic fuel control.