Dear Nice effort, but I have doubt over two answers.

1. Who started Namaz e Taraweeh?

Taraweeh Prayer was started by Holy Prophet Muhammad S.A.W.W.
Hazrat Umar R.A. make people offer 20 Rakats before 1 Imam, instead of offering in groups in Masjid e Nabvi S.A.W.W.


2. Number of Muslims in Badar?
you said 333, but I think there were 313.


AND ALLAH SWT KNOWS BEST.