No. There is no single narration that the Prophet ever led Taraweeh neither in Sunni nor in Shia books. Taraweeh was initiated in the year 14 after Hijra by Umar Ibn Al-Khattab as he himself called it a Bid'ah and said it is a good Bid'ah. (Saheeh Al-Bukhari, Salat Al-Taraweeh.)
Yes it is better to pray with congregation than praying alone even if the congregation is with Sunni Muslims. When you pray in congregation with Non-Shia Muslims, you need to recite Al-Hamd and other Sura yourself but with out clear voice.
Eid Prayer is allowed to be prayed in congregation because it is in its original form an obligatory prayer in the presence of the Prophet (SAWA) and the Imam (AS). It is not like Salat Al-Lay or Nafila or Ghofaila etc which is always recommended. The reason behind praying Eid Namaz in congregation is its original form which is Wajib.
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