Is initiating rising from prostration when the Imam stands, without the forehead touching the ground, considered anticipating the Imam, which is forbidden, or is it obligatory to complete the prostration before rising?

It is prescribed for one who joins the prayer late (masbūq) to join the Imam in whatever posture he finds him, and not to wait for him to stand for the next rak'ah. This is based on the Prophet's (peace and blessings be upon him) saying: "If you come to the prayer and we are prostrating, then prostrate and do not count it as anything. And whoever catches the rak'ah has caught the prayer."

If the one who joins late says "Allahu Akbar" while the Imam is prostrating, and then he lowers himself to join him in prostration, but the Imam raises his head before the follower places his forehead on the ground, then he should rise with the Imam and not prostrate. He should then wait and not fully sit or stand until the Imam has settled into his position, and then he should settle into his position after him.