1- Yes it’s permissible. The only exception is reciting the verses of mandatory sujud, which are Sajdah 15, Fussilat 37, Najm 62 and Alaq 19.
3- If she comes across a verse that contains a wajeb sajdah, and she is reading in Arabic, she must skip reading it. The sajdah does not require purity, so she can perform it right away.
If she did not, then yes now she makes it up. This is assuming she read it in Arabic. If she didn’t read it in Arabic then she doesn’t have to make the sajdah.
4- No she is not
5- Yes she can