Is the circulated story true about the Prophet's (PBUH) prayer in the Al-Kou' Mosque located in Taif, and the stopping of the rock that the polytheists wanted to throw at him during his prayer after his Tashahhud? And is visiting this mosque and praying in it considered an innovation (Bid'ah)?

There is no knowledge of the mentioned story in Islamic collections. The Permanent Committee has issued a fatwa (definition) stating the impermissibility of visiting the Elbow Mosque (Masjid al-Kūʿ) in Taif and of organizing student trips to it, due to the misguidance it entails for the youth. The duty is to safeguard beliefs from innovations and deviances.