What is the ruling on the prayer of one who leaves their prayer to open the mosque door for worshippers, and what is the ruling on the prayer of one who adds an extra rak'ah?

The jurists have agreed that much continuous action in prayer invalidates it. If the steps taken by this person to open the door and return were few, then his prayer is valid. However, if they were many and continuous, his prayer is invalid, and he must repeat it.

As for the prayer of the first person, concerning an extra rak'ah: If he missed a rak'ah and was unable to catch up with the Imam, and then performed a rak'ah in its place after the Imam's tasleem, there is nothing wrong with that. However, if he performed an extra rak'ah because he left the row and opened the door without having missed a rak'ah, then his prayer is invalid, and he must repeat it.

As for interrupting the prayer: If it is an obligatory prayer (fard), it is not permissible to interrupt it. If it is a supererogatory prayer (nafilah), there is no harm in doing so. Therefore, if he interrupted an obligatory prayer, he has erred, but there is no sin upon him as long as he was ignorant. His prayer is valid if he returned and began the prayer with the Imam and completed what he missed after the Imam's tasleem. If it was a supererogatory prayer, there is no harm upon him in interrupting it and resuming it after fulfilling his need, completing it without considering what preceded from it.