Is reciting bismillahir rahmanir raheem before alhamdu in namaz obligatory?

1. Is reciting bismillahir rahmanir raheem before alhamdu in namaz obligatory? If one doesn't read bismillah before alhamdu, either in the first or second, third or 4th rakaat is their salah nullified?

2. Is reciting rabbigh firli in between sajadah obligitory? If one doesn't recite this inbetween sajda and just says subhana rabbiyal a'ala in sajadah and sits and says Allahu akbar and then goes into sajadah again and says subhana rabbiyal a'ala, is this incomplete and is the namaz nullified because the believer didn't say rabbigh firli between the sajadah?

3. Is it obligitory to say bismillah before or after any surah during namaz? If one doesn't, is their namaz invalid?

4. If a woman reads silently where her lips and tongue is moving but you cannot hear her, are her prayers invalid? She lives in a joint family, where her husband's cousins, both male and female come and go and she cannot say for sure who is at home and who isn't. It is a 3 floor house, with she occupying one room and the opposite room belongs to her husband's uncle and her husband's cousins.

5. If a woman has been praying normally but hasn't been saying bismillahir rahmanir raheem before surah fatiha (as in scenario 1) and hasnt been saying rabbigh firli in between the sajadah (scenario 2) and hasnt been saying bismillahir rahmanir raheem before or after any surah in namaz (as in scenario 3), and has been reading quietly and has been moving her lips and tongue and no one is able to hear her, has all her namaz been invalid if she has been praying like this? She was unaware that a woman is to pray aloud she knew reading quran should be read in a tone one can hear themself but she didnt know you are suppose to hear yourself during namaz