What is the ruling of Islamic law regarding my continued marriage to a Muslim woman who recently converted to Islam, given that I discovered her dishonesty in several matters, and what is the optimal course of action in this situation?

You have done well by marrying her to help her with her religious matters, and to teach her the Qur'an and the Arabic language. If she lied, then she has done wrong, for lying is a grave sin. Do not think ill of her in every matter, for the default state of a Muslim is integrity, especially with her good qualities. It is not permissible to spy on her unless there is suspicion, and deal with her based on what is apparent. You can inform her of your knowledge of her lie to encourage her to be truthful and to caution her against lying. It is advisable to emigrate with her to a Muslim country due to the benefits therein, such as removing her from her family's environment and facilitating the custody of children in case of divorce.