What is the ruling on not performing the Fajr prayer on time due to an ink remover and forgetting the possibility of making it up in the school mosque, and what should be done to alleviate the sadness over missing it?

If the mentioned deodorant has a substance that prevents water from reaching the skin, it must be removed. Otherwise, mere color does not invalidate the prayer. If prayer must be redone, it can be performed in any pure place. If you forgot to perform it until the time expired, there is no sin, and its expiation is to pray it whenever you remember. If you intentionally left it, you have committed a great sin, but sincere repentance erases the sin, for Allah accepts repentance and pardons evil deeds. Perform the missed prayer if you have not already done so, have a good opinion of Allah, and strive in worship and good deeds.