AKB has posted Ahadith that show Prophet pbuh did pray tarawih for 3 nights in Ramadan and people prayed behind him (in congregations). People WERE praying Tarawih in small groups as written in Hadith you posted, all Omer ra did was to ask them to pray under one Imam instead of small groups, how does this become a Bida'ah?
Rasoolullaah pubh cried once on Shahadah of Imam Hussain (according to some narrations) , now if some people cry every year on the same day in large congregations, is this a Bida'ah?
I dont understand the question of "EVERY YEAR". there were events happened in history which occurred only once. but people remember them in different ways every year in those dates. How come remembering an event a Biddah. Remembering things which happened in the past time is natural phenomena, nobody can stop it. Prophet remembered that event once (when the actual event did not occur) and cried and showed others that it will not be a happy moment for muslims, but those muslim who wear fancy dresses and celebrate it with fasting; (when Imam hussain was not fasting). It looks odd to me. Crying is the higher stage in expressing emotions of grief, Do you think those people who dont show the feeling of grief when they listen or think about this incident can be true muslim. and do you think they have feeling of love toward our prophet Muhammad pbuh.
Sunni Sources of Ahadith (not the shia sourse) shows that Prophet pbuh did pray A PRAYER (not named as Tarawih). for 3 nights, and people did pray behind him.
Since it is Sunni source it is not a convincing proof for Shias. Since it is proven that prophet did not continue it after that it is a convincing proof that todays Sunnis tarawih is not valid, even if it was revived by 2nd Khalafat in his last years of Khalafat.
It was not started by 1st Khalafat either, in his time. People were continually praying tahajjat prayer in the latter part of night in a non-congregational form.
4th Khalfat stopped in his capital city of Kufa during his time.