What is the Shar'i ruling on competing with the Imam in prayer, and must the congregant wait until the Imam places his forehead on the ground before prostrating, and what should the congregant do if he coincided with the Imam in prostration but became aware before prostrating?

It is not permissible for the congregant to precede the Imam intentionally. As for lagging behind him, it may or may not invalidate the prayer. Equaling the Imam in actions is disliked but does not invalidate the prayer. And whoever coincides with the Imam in prostration or the like should not return, rather returning is only for one who prostrated before his Imam or rose before him.