Does Allah's knowledge emanate from His essence or from the informing of the angels, and is it permissible to supplicate in secret with what Allah will not hold us accountable for from the whispers of the soul?

One must believe that Allah Almighty is characterized by absolute, eternal knowledge. He is "the Knower of the unseen, from whom not even the weight of an atom is hidden." His knowledge is not acquired and does not need angels. The benefit of recording deeds is for humanity, to deter them from sins and to establish proof against them on the Day of Judgment. As for supplication (du'a), it is not considered a supplication except by uttering it, whether secretly or openly. Thoughts that merely cross one's mind are not considered supplication.