I am not discussing the matam or ashura here, its just an example about what constitutes Bida'ah and what not.
1- Sunnis have not tried to convince you, you are trying to do that.
2- Second Khalifa did not "revive" it, Hadith clearly shows that people "did" pray tarawih even during teh time of Abu Bakr a , look at the qoute from Hadith posted OP
It shows people prayed them during and after Prophet pbuh. Hence its very clear that it is valid.
As for the name "tarawih" i don't know the exact origin of it, you can call it anything doesn't matter. 3- Can you show me the source of your statement that Hazrat Ali ra stopped it?
All I hear is rhetoric and not arguments.
People used to pray in Ramadan in the time of the prophet (SAW) and the night prayer talked about time and again are Tahajjud prayers, which is a sunnat-e-mukadda and mentioned in Quran as well.
We find no such reference to a prayer called tarawih except in teh hadith where Umar called it Bid'a.
Sunnis are trying to defend tarawih a biddat
It said people continued praying individually and mostly at home just as teh Prophet (SAW) ordered. No one is disagreeing with reading Quran in Ramadan.
"....... I ordered people that they should only gather for Fardh (obligatory) prayers during Ramadhan, and told them that congregation (Jamah) in Nafal (i.e. Tarawih) is a Bidah (innovation) then all of these people started shouting that Sunnah of Umar has been changed.
Rudhutul Kafi, Sermon of Al-Fatan wa Al-Bidah