Answered by Shaykh Faraz Rabbani
Is it necessary to say “bismillah” quietly before every surah recited in prayer?
Before the fatiha, it is a confirmed sunna.
Before reciting a complete sura (from the beginning), it is not a confirmed sunna, but good [=recommended] to do. [Durr+ Hashiya]
When reciting in prayer should the lips move (even in a silent prayer)?
Without this, your prayer would be invalid (unless praying behind an imam, wherein one does not recite).
When following an imam should one say the takbir after the imam at the various points?
It remains a confirmed sunna to pronounce all the dhikrs of the prayer when praying behind the imam, though it is prohibitively disliked (makruh tahriman) to recite any Qur’an behind him, even the Fatiha, even in silent prayers.
When doing makeups in the mosque, say just before the start of another prayer, is it necessary to do the azaan and the iqama?
(See recent post on giving the adhan and iqama for makeups.)
One may leave it out in the masjid if reciting them quietly would make even some people aware that one is performing makeups. It is a sin to reveal one’s past sins.
And Allah knows best.