Is the prayer of one who is led by an imam valid if he is sometimes unable to hear him or if he delays completing his prayer after the imam has finished, and what is the correct action to take in this situation?

There is no harm for worshippers to perform prayer outside the mosque when it is full, as long as they can hear the Imam's voice or see him, or see someone who sees him from among the congregants. If the sound is cut off from them and they do not see the actions of any of his congregants, they should complete the remainder of their prayer on their own. The prayer is valid and they are not required to repeat it. The correct action is what they did, which is praying outside and following the Imam if it is possible to know his transitions, otherwise, they should complete the remainder of their prayer individually, or put forward someone to lead them.