'flight idle' is a few % higher than 'ground idle', basically a different power setting.
'Beta Range' can be translated as reverse, or negative blade pitch. This is controlled by the power lever (although it is basically a blade pitch change) in order to be sure of the engine being in idle before reversing.
I'ts been a while, but i also remember the condition lever having two detents, high and low idle, basically only used for cross-engine starting in hot&high conditions. PT6-61 (cheyenne pa42)
regarding flat- and derated engines:
relative to outside air temperature:
flat rated meaning the engine is rated to a certain power limit, before reaching itt limits for example. On reaching an ambient temperature which leads to egt limitation, this will be the limiting factor, thus leading to less power available.
a de-rated engine on the other hand, is limited to an itt of say 700°c, even though the manufacturer limit might be 750°c. This reduces maximum available power throughout the whole temperature range.
I stand to be corrected! (excuse my stumbling english!)