It's connected to the night. I can only access the ceremonial suit and the powers related to it after sunset. Also, the powers become stronger and weaken depending on the phase of the moon. On full moons, I'm the strongest.
Erm.... not sure what the connection is between his power and the Duat. From what Tawaret told me, the place where you go after you die is... all connected out there, but there's separate areas for different peoples and pantheons. I always understood Khonshu's power is his own... and gods become stronger the more they are worshipped? Honestly, I never thought to ask.