Is placing the hand on the forehead after prayer and reciting the supplication, "In the name of Allah, there is no god but He, the Most Gracious, the Most Merciful. O Allah, remove from me worry and sorrow," a Sunnah? And is it permissible to act upon a Hadith if it is weak?

The Hadith in question is very weak, and Al-Albani ruled it to be so. Its wording is: "When he prayed, he would wipe his head with his right hand and say: 'In the name of Allah, there is no god but He, the Most Gracious, the Most Merciful. O Allah, remove from me anxiety and sorrow.'" Therefore, it is not established.