How can I combine performing Fajr prayer with attending lessons at the local mosque, given that I am 16 years old?

Strive to wake up for Fajr prayer and attend scholarly gatherings, as long as it does not affect your studies. If your parents prevent you, explain to them gently that this does not conflict with your academic excellence, but rather aids it. There are other means of learning, such as websites and audio lessons. Strive in supplicating to Allah to grant you beneficial knowledge and righteous deeds.