Must prayers be redone after ghusl for menstruation if the intention was not made during ghusl, and it is not recalled whether ghusl was redone with intention later? And is it permissible to give in charity a notebook taken from a boy before puberty that was not returned to him?

There is no validity to doubt in an act of worship after its completion. Therefore, doubt after completing ghusl (definition) (ritual bath) does not affect its validity. The ghusl performed by the questioner is sufficient, and she is not required to repeat it, nor to repeat the prayer. The place of intention is the heart, so a mere resolve to perform the act is sufficient. As for giving the notebook in charity on behalf of its owner, it is correct if it is impossible to return it to him; otherwise, it is not permissible. In such a case, it is obligatory to return it, or seek his permission for the charity, or pay him its value.