Is it permissible for a student studying in America to pray in the library, in order to make use of study time, bearing in mind that this could be a means of da’wah (inviting others to Islam)?

Congregational prayer is obligatory for a capable man who hears the call to prayer under normal circumstances. However, you are not required to go to the distant mosque whose distance you mentioned. Furthermore, being engaged in studies is considered a permissible excuse for missing congregational prayer if abandoning the studies would result in significant harm. You are permitted to pray inside your school, either in congregation with your colleagues or individually, and you will be rewarded with the merit of congregational prayer in the mosque as long as you have a valid excuse.