Does the prayer of an Imam become invalid if he bowed after Surat Al-Alaq, then performed the prostration of recitation (sujud at-tilawah) after he had already bowed, in order to allow the latecomers to catch up? And what should he have done in those two situations?

If a worshipper or an Imam, whether forgetfully or intentionally, bows (performs ruku’) after a prostration of recitation (sajdat al-tilawah), it is not permissible for him to prostrate afterwards, because this would add an extra pillar to the prayer (bowing twice) and disrupt its proper form.

The Imam’s prayer becomes invalid if he does this while aware of the ruling, but it is valid if he is ignorant.

As for the congregants (Mamu’moon): - If the congregant knows that the Imam bowed (performed ruku’) and then prostrated for recitation (sajdat al-tilawah), it is obligatory for him to separate from the Imam. Otherwise, his prayer becomes invalid if he was aware of the Imam’s error and his own error, and he must repeat it. His prayer is valid if he was ignorant. - If the congregant did not know and followed his Imam, his prayer is valid in all cases.

If the Imam did that based on the belief that it is valid in his madhhab, then his prayer is valid, and the congregants’ prayer is valid in all cases, and the congregant must follow his Imam.