Question 3: Assalaamu alaykum.
I notice some of the masjids in my locality recite a specific thikr after every four rak’ahs of Salatul Taraweeh, just wondering if this is from the sunnah?
I am not aware of a Sunnah about doing any specific Dhikr after 4 rak’ah of Taraweeh. What I do recall is that the Prophet (s.a.w) prayed the night prayer in intervals of 4 rak’ah, meaning prayed 2 then 2 more then a little rest and then back again. But not aware of any specific dhikr in the rest time. Allah knows best.