Is it permissible for a Muslim to begin his supplication by saying: "O Allah, You have said, and Your word is the truth: 'Call upon Me humbly and secretly,' O He who sees the black ant on a dark night, O Allah, You see my place and hear my words," and then supplicate for whatever he wishes?

There is no harm in you saying, when supplicating, "O Allah, indeed You have spoken, and Your word is the truth," and then reciting what Allah Almighty has said. What was mentioned in the question regarding verses is incorrect, and the correct verses are His Almighty's saying: "And your Lord said: 'Call upon Me; I will respond to you'" (Ghafir: 60) and His Almighty's saying: "Call upon your Lord humbly and privately" (Al-A'raf: 55). However, it is better, more appropriate, and more beneficial to supplicate with the supplications reported from the Book of Allah Almighty and the Sunnah of His Messenger, peace and blessings be upon him.