As reciting the Quran when in Sujood is prohibited, if a person knows some ayahs from the Quran that are Duas, like in Dua of Adam or last verses of surah Imran, can a person then recite those in humiliation with the intention of asking forgiveness? Or should a person refrain from it?

Ustadh AbdulAziz al-Haqqan

Yes, it is allowed when you say them with the intention of duʿāʾ, not recitation.