What is the ruling on someone who arrived late for prayer and found the Imam prostrating, and did not know which rak’ah the Imam was on, so he raised his head and back slightly to ascertain the position of the Imam and the congregants? Does this count as an excessive movement that invalidates the prayer, especially if it did not take as long as the duration of ṭuma’nīnah (tranquility)?

The Sunnah is for the latecomer to join the Imam in whatever posture he finds him in. He says the Takbirat al-Ihram (opening Takbir) and then follows the Imam. If the Imam rises from prostration, the follower must follow him. If the follower thinks the Imam has stood up and then moves, but then realizes that the Imam has not stood up, he must return to where the Imam is. There is no sin upon him for this, nor is he required to perform the prostration of forgetfulness (Sujud al-Sahw), because merely shifting one's position does not invalidate the prayer intentionally.