Is it permissible for a menstruating woman to utter the two Shahadas and perform ghusl to embrace Islam? And is it permissible for her to attend Eid prayers, dhikr, and give charity, or should she wait until her menstruation ends to convert?

A woman is not permitted to delay her conversion to Islam until she becomes pure. Rather, she must pronounce the two Shahadas immediately. She should attend the Eid prayer to listen to the sermon and say "Amin" to the Imam's supplication, while remaining separate from the prayer area.