In the anime 少女革命ウテナ (Revolutionary Girl Utena) one of the shadow girls often says
which is translated in the subtitles as "I wonder, I wonder. Do you know what I wonder?".
I'm familiar with adding かしら after the predicate but I've not come across it as a standalone word before. Is this usage standard? If someone asks me, for example, "do you think my cunning plan will work?", and I'm not sure of the answer, can I just respond with かしら? It feels unlikely to me.
Unrelated, but I also have no idea how ご存知 works in this phrase.