Is it permissible for me to pray at home instead of the mosque due to its distance and the prevalence of evils therein, while still committing to Fajr and Jumu'ah prayers?

Congregational prayer is obligatory for adult men, and it is not a condition to perform it in the mosque. If you pray it in your home with your family, the sin is lifted from you, but you miss the virtue of witnessing the congregational prayer in the mosque. The Sunnah is to witness the congregational prayer in the mosque. The presence of evil acts should not prevent you from doing what Allah has legislated for you. What is obligatory upon you is to lower your gaze, and you are not sinful for what your eye unintentionally falls upon, but you should promptly avert your gaze. The most preferable and complete act is to witness the congregational prayer in the mosque and lower your gaze. If you pray in your home congregationally, you are not sinful, but you miss out on the virtue.