What is the solution for the feelings of hypocrisy, boasting, and seeking to please others when performing prayers in the mosque, and do these feelings render the prayer unacceptable?

Your determination to be steadfast and perform prayers in the mosque is correct and good, for which you will be rewarded. Convince your father to permit you to pray Fajr in the mosque. If he insists on preventing you, then pray in congregation at home. What you feel regarding hypocrisy is a whisper from Satan to hinder you from doing good, so do not pay attention to it. Strive for sincerity to Allah by being mindful of His awareness and observation of you, and that He alone glorifies by His praise and demeans by His censure, and that people can neither harm nor benefit. Beware of abandoning good deeds for fear of showing off; rather, sincerity and action are both necessary.