Answered by Shaykh Abdurrahman ibn Yusuf Mangera
Reciting Qur’anic supplications in prayer
In the name of Allah, the Inspirer of truth.
Assalamu alaikum wa rahmatullah
According to the Hanafi school, one can make any du’a one likes from the Qur’an (or the hadith) after salutations on the Messenger of Allah (upon him be peace) in the final sitting of the prayer (Al-Durr al-mukhtar 1:351-2).
Other than this, it is permissible for a person who is praying alone to make these extra du’as in the ruku’ and sajda of optional prayers, but not in obligatory prayers (Radd al-Muhtar with Al-Durr al-mukhtar 1:366).
And Allah knows best.
Wassalam
Abdurrahman ibn Yusuf