What should a questioner do when he goes to the mosque and prays in a manner consistent with the Prophet's hadiths, then notices the glances and astonishment of the worshippers; should he stop going to the mosque, or continue his prayer and not care, or pray as they pray to avoid the glances and his feeling of showing off?

Prayer in the mosque is not optional. The Prophet (peace be upon him) even intended to burn the homes of those who failed to attend it. It is obligatory upon able-bodied men and is among the causes of a good ending. People staring is not an excuse to abandon congregational prayer; rather, one must continue to go to the mosque and repel the feeling of showing off, for abandoning an action because of people is showing off.