Does looking to the right to read the Qur’an from the Mushaf invalidate the Qiyam al-Layl prayer, knowing that placing the Mushaf in front of me does not enable me to turn its pages, and it has been reported that one’s gaze should be directed to the place of prostration?

Your prayer is valid, and looking at the Mus'haf does not invalidate it. Reciting from the Mus'haf is permissible in supererogatory (nafila) and obligatory (fard) prayers, according to the preponderant opinion. As for looking at the place of prostration, it is recommended, not obligatory. Scholars have differed on the exact place to look during the standing (qiyam (definition)) posture, but they have not differed on the validity of the prayer of one who does not look at the place of prostration.