Is the Imam's repetition after every prayer of "I bear witness that there is no god but Allah; I seek forgiveness from Allah; We ask You for Paradise and seek refuge in You from the Fire" three times from the Sunnah, and what are the other authentically reported supplications after the prayer?

The Prophetic Sunnah (definition) does not contain specific supplications (du'as) or remembrances (adhkar) for the month of Ramadan (definition), with the exception of the supplication for Laylat al-Qadr (the Night of Decree): "O Allah, You are Pardoning and You love to pardon, so pardon me." As for designating adhkar with specific numbers or particular rewards for the blessed month, this has not been reported. Rather, it is recommended for a Muslim to increase in the remembrance of Allah and supplication at all times, especially during times when supplications are answered. One must be cautious of what circulates regarding supplications and adhkar for each day of Ramadan, as these are human inventions and not from the Sunnah. A Muslim should strive to adhere to the legislated adhkar and to recite and ponder the Qur'an.