How can we reconcile Allah’s saying: "And We have certainly adorned the nearest heaven with stars" with what is mentioned in the Holy Quran about the existence of seven heavens, given the modern scientific proof of the existence of seven heavens, and that the seventh heaven is the one that contains the stars?

The questioner did not mention two contradictory verses. Rather, the verse: {And We have certainly adorned the nearest heaven with stars} [Al-Mulk: 5] is consistent with other verses indicating that the sun and stars are in the nearest heaven. What is understood from the apparent meaning of the Qur’an does not contradict modern science. The interpretation of "ad-dunya" as the nearest of the heavens is the apparent meaning, and it is supported by the Hadith of the Mi'raj (Ascension) which shows that the Prophet, peace and blessings be upon him, began with it. We believe in the existence of stars in the nearest heaven, as is apparent from the texts. The existence of the seven heavens is established, but their established existence does not mean that the stars are in them, and no text has been reported indicating the existence of stars within them.