What are the recommended supplications (Du'as) and remembrances (Adhkar) after performing the night prayer (Salat al-Layl), and after the forenoon prayer (Salat al-Duha), and for the Ruqyah (Islamic exorcism) and the Mu'awwidhatayn (the two surahs of refuge)?

There is no specific supplication to be recited after the Night Vigil Prayer (Qiyam (definition) al-Layl) except for the saying of "Subhanal-Malikil-Quddus (Glory be to the King, the Most Holy)" three times after concluding the Witr prayer, raising one's voice on the third repetition. It is recommended for a Muslim to supplicate with whatever authentic supplications and others are easy for him, especially seeking forgiveness (istighfar). As for after the Duha prayer, no specific glorifications have been reported.