How can I respond to an atheist who asks for proof that God knows what is in the innermost thoughts, that He does not lie, and that He neither begets nor is begotten?

The existence, knowledge, and truthfulness of the Creator, and that He neither begot nor was begotten, can be proven by both rational and transmitted evidences. The entire universe points to the Lordship, Oneness, and wisdom of the Creator. As for the invalidity of the claim that creatures created themselves or came into existence without a Creator, this is self-evident to reason. It is inconceivable that the Creator would not know His creation, for He is Al-Latif (the Subtle), Al-Khabir (the All-Aware), Who created everything. Likewise, the All-Knowing Creator cannot lie, for His word is truth, and there is no discrepancy or contradiction in His Book. Furthermore, Allah did not beget, as He has no consort, and because He is free of need for a child who would be for assistance or to remedy incapacity. Also, He was not begotten because He has no need for anyone to bring Him into existence, for His existence was not preceded by non-existence.