Qavion
The 25% maximum thrust reduction is for all engines, and is defined in the FAR's.
It is permitted to reduce a fixed derate (TO1, TO2) by another 25%.
The thrust reduction selections on the 777 are identical to those on the B744.
You can input an assumed temperature of 99°C, but the FMS will reduce this to:
a: AFM limit, 54°C or 69°C (this is an option.)
b: 25% reduction off the rating in use.
I do not know if the FMS compares takeoff thrust with climb thrust for any other reason than to use the appropriate CLB thrust for the Takeoff rating in use.
Mutt