What is the ruling on praying Tarawih in congregation at the mosque, nine rak'ahs with a tashahhud after the eighth and another after the ninth, followed by the taslim, along with the evidence and sayings of the scholars?

The best way to pray Tarawih is eleven rak'ahs, as the Prophet, peace and blessings be upon him, used to do. As for the manner mentioned in the question—nine rak'ahs prayed continuously with one tashahhud in the eighth and one salam after the ninth—this is one of the confirmed descriptions of the Witr prayer narrated from Aisha, may Allah be pleased with her, and not for the Tarawih prayer. There is no contradiction between this description and the hadith "Night prayer is two by two," because the hadith pertains specifically to the night vigil prayer (Qiyam al-Layl), whereas the nine rak'ahs are for Witr.