Communal du’aa’ after Taraaweeh prayer

With regard to the first part of your question, please see the section on Taraaweeh prayer and Laylat al-Qadr under the heading of Fasting on this website. 

With regard to communal du’aa’ after Taraaweeh prayer, this action is an innovation (bid’ah). The Prophet (peace and blessings of Allaah be upon him) said, “Whoever does an action that is not part of this matter of ours (Islam), will have it rejected.” Narrated by Muslim, 3243. 

What was narrated from the Prophet (peace and blessings of Allaah be upon him) was that after Taraaweeh prayer he would say, “Subhaan al-Malik al-Quddoos (Glory be to the Sovereign, the Most Holy)”, three times, raising his voice on the third time. 

Ahmad (14929), Abu Dawood (1430) and al-Nasaa’i (1699) narrated that Ubayy ibn Ka’b (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) used to recite in Witr “Sabbih isma Rabbika al-A’la (Glorify the name of your Lord, the Most High)…” [i.e., Soorat al-A’laa 87] and Qul yaa ayyuha’l-kaafiroon (Say (O Muhammad), ‘O al-Kaafiroon (disbelievers))…’” [i.e., Soorat al-Kaafiroon 109] and “Qul Huwa Allaahu ahad (Say (O Muhammad), ‘He is Allaah, (the) One)…” [i.e., Soorat al-Ikhlaas 112]. And after he said the tasleem he would say “Subhaan al-Malik al-Quddoos, Subhaan al-Malik al-Quddoos, Subhaan al-Malik al-Quddoos (Glory be to the Sovereign, the Most Holy; Glory be to the Sovereign, the Most Holy; Glory be to the Sovereign, the Most Holy)”, raising his voice. Classed as saheeh by al-Albaani in Saheeh al-Nasaa’i, 1653. 

Then in Witr prayer the imam will recite du’aa al-qunoot and the worshippers will say Ameen behind him, as Ubayy ibn Ka’b (may Allaah be pleased with him) used to do when he led the people in praying Taraaweeh at the time of ‘Umar (may Allaah be pleased with him). So there is no need to introduce this bid’ah. How true are the words of the one who said, “All goodness is in following those who came before, and all evil is in the innovation of those who came later.” 

And Allaah knows best.