However, there're one part that said the FCC send the various data such as
the N1 or EPR trim, Bleed Config, Flap position, Weight on nose wheel, GMT, and DATE.
Input in and out is what you are confused about. The FCC's sense some of this data (flap position being it"s only real job as you listed) to coordinate with other systems.
GMT is the abbreviation of what you spoke of.
If so why the engine require those information in order to operate?
The engines do not require the FCC's to operate.
Also, for a given throttle setting as the environment around the engine has change.
Does the FADEC advance the engine RPM automaticly according to the throttle position?
For example, if throttle is at about 80%, engine in climb rating and when the
plane climb the N1 limit is lifting and the FADEC order the engine to speed up
in order to maintain the 80% thrust rating.
Do not confuse thrust and N1, N1 is a fixed value, if selected it will maintain 80% N1, thrust is not accounted for as temp/alt change actual thrust. N1 is engine speed thrust is engine production.
Does the FADEC manipulate the bleed valve [either LP or HP or both] in
order to maintain the minimum air pressure that the system need or the
HP valve just kick in if the anti ice is use or the N2 is drop below the setting value like the B767.
The PSC's control bleed shift.