The FADEC does not manipulate the LP or HP bleed valve on the engines but it does regulate N2 speed to maintain a compressor discharge pressure of 48 PSI. This is based on the throttle position, ambient pressure and N2 speed lever in order to enable the engine to deliver sufficient air pressure for the aircraft pneumatic system to work.
If I remember well, the N1 TRIM signal is supplied from the FCCs to compensate for slight mismatches in throttle resolver angles and still set the same thrust on all 3 engines, it only works with the levers above a certain setting. (the pilot / Auto Throttle does not have to perfectly align the levers, this is achieved by the trim signal)
The GMT and DATE are used by the ECU for fault history logging; in a backshop the ECU can be hooked up to a computer and the operating hours and fault history can be read to great detail, on the aircraft through CFDS the fault history and current faults can also be checked.
The tail engine is supported in the same way as the wing engines are mounted; by a pylon. That makes the 3 engines interchangeble (with some work) The structure you see above the "tunnel" and below the fin is that pylon structure.
It is quite a sturdy construction attached to 4 "banjo shaped" fittings that run from the fuselage and also act as the fin attachment base.
The last part is a fairing that houses the pre-cooler and pneumatic ducting that runs back to the airframe.