Is there any sin upon me for praying Tarawih at home, listening to the Imam of the Grand Mosque in Mecca via the radio, with the intention of improving my Quranic recitation and increasing the number of rak'ahs, and not with the intention of following him in congregational prayer?

A woman's prayer in her home is better than her prayer outside it. It is not permissible for her to follow the Imam via radio alone, due to the lack of devotion that results from it. Her prayer may even be invalid according to some scholars because of the absence of the intention to follow the Imam.