How sound is the aforementioned marriage supplication, which includes writing a Qur'anic verse on the hands, and saying a specific dhikr while raising the hands to the sky?

This supplication is invented, and its method is an innovation and denounced. It contains ambiguous phrases. It is not permissible to engage in such things, for the supplications in the Quran and Sunnah are sufficient and fulfilling. The Messenger of Allah, peace and blessings be upon him, used to prefer comprehensive supplications. Examples of this include: "Our Lord, grant us from our spouses and our offspring comfort to our eyes and make us leaders for the righteous" and "O Allah, I ask You for guidance, piety, chastity, and richness."