Is the prayer called "Salat al-Shukr" (Prayer of Gratitude), which is performed five times daily, before each obligatory prayer, and in which one prostrates after the final tashahhud and before the taslim to repeat "Praise be to You, and thanks be to You, and forgiveness be to You" twenty times, Islamically valid?

There is no prayer of gratitude (Salat al-Shukr) in the Sunnah (definition); rather, there is a prostration of gratitude (Sajdat al-Shukr) upon receiving a blessing or repelling an affliction. The prayer mentioned is incorrect due to the extra prostration after the Tashahhud (definition) and before the Taslim (definition), which invalidates the prayer. There is no supererogatory prayer after the break of dawn and before the Fajr prayer, except for the two rak'ahs of Fajr.