>and it wasn't written in ball-point pen
It wasn't, according to BKA in Germany.
Only additional EDITORIAL notes were written using a ball-point pen.
>Also, if the Nazis were so bad, why did they allow her continue writing it in and not disposing it?
Implying the Nazis were omnipotent and were able to see everything happening anywhere. They weren't.
If you get put into a nice comfy Covid-19-camp, you may figure that out yourself.