Should women pray the Taraweeh and the rest of the prayers in the mosque or at home?

A woman should pray Taraweeh wherever she likes. If she wants to pray at home, she can, and if she wants to go to the mosque to find strength and support by being with her sisters and brothers in worshiping God, then she can. The point is not the location, as a woman should pray where she finds her heart in humility towards God. Imam al-Shafi’i was of the opinion that praying Taraweeh in the mosque or at home is equal in reward for both men and women.
Accordingly, a woman cannot be prevented from going to pray in the mosque either for attending a lesson, for praying Taraweeh, or for reciting the Quran. This is what our Prophet (peace and blessings be upon him) taught us when he said to men, “Do not prevent the slave women of God [i.e. women] from the houses of God.” The statement of the Prophet (peace and blessings be upon him) addressing women, “Your prayer at home is good,” is based on the preference of women to be protected and veiled.
And God Almighty knows best.