Does Allah Almighty bring to mind His other information while doing something or speaking with the angels, or does He not bring it to mind because He does not need to think about it like humans?

These thoughts are based on likening Allah Almighty to His creation, and Allah, the Most High, is not resembled by anything. Allah Almighty says: "There is nothing like unto Him, and He is the All-Hearer, the All-Seer." Allah Almighty is not distracted by one matter from another; He holds people accountable, provides for them, and hears their supplications all at once. He is not confused by the diversity of issues, languages, and needs. Sheikh al-Islam Ibn Taymiyyah mentioned that Allah’s accountability of people on the Day of Judgment is like the sight of the moon on a full moon night; everyone sees it individually. Ibn Abbas was asked how Allah holds people accountable in one hour, and he said: "Just as He provides for them in one hour." Allah hears the words of every worshiper reciting Al-Fatiha and responds to what they say in it, and that does not incapacitate Him. His Kursi (Throne) encompasses the heavens and the earth, and He is not wearied by their preservation, so how could He be wearied by knowing about them, hearing their words, or answering their prayers? These whispers should be repelled and not given attention, for Allah has forgiven this nation for what they think within themselves, as long as they do not act upon it or speak of it. Therefore, if the intention to commit a sin is merely a fleeting thought that did not settle in the heart, it is forgiven, and a Muslim will not be held accountable for it. Such negative thoughts indicate clear faith.