Did God punish women with menstruation because of Mary, upon her be peace, when she gave birth in a bloody labor on the trunk of a tree? And what is the sin of the other women in that?

What you mentioned, that menstruation was due to Mary, peace be upon her, is false and has no basis. Menstruation is decreed for the daughters of Adam since their creation. It has been reported that menstruation was first cast upon the Children of Israel as a punishment for them, as 'Abd al-Razzaq narrated from Ibn Mas'ud. Al-Hafiz mentioned in Al-Fath that it is possible to reconcile this with menstruation being general among all daughters of Adam by understanding that its duration was prolonged for the Children of Israel as a punishment for them, not as an initial cause for its existence. It has also been narrated from Ibn 'Abbas that menstruation was upon Eve after she was cast down from Paradise.