There is a bachur in the yeshiva who r”l had a stroke, cannot daven on his own, and someone stands next to him and davens out loud to be motzi him. Sometimes the bachur comes late (he has an aide who brings him).
What should I do if I am supposed to daven with him but he is late (I am makpid to start SE with the minyan, as otherwise it is a shaila if it is tefilla btzibbur, plus it is very distracting for me because I keep thinking, “Is he coming, is he not coming, how late will he come”?
Could I just start davening on my own (if he is more than a minute late), even though now he won’t have anyone to be motzi him? How long should I wait? Plus, in order to reach his place, he walks in front of people who are davening. What should be done?
At the time that you are davening with him you are osek b’mitzva, therefore you are patur from davening with a minyan. Therefore you don’t have to be worried that you are missing tefillah b’tzibbur. If you can make it, that is great, but if you don’t there is no need for concern, especially if you are getting some sort of tefillah b’tzibbur. If you will be calm knowing that whatever happens with him, you are still alright, you won’t be anxious regarding the tefillah b’tzibbur, and it won’t ruin your concentration.
As far ass your other question, if there is no one else to daven with him, (this is your day), then you should daven together with him and do the chesed, and not daven with the t’zibbur, as you are now involved with a mitzvah.
Regarding the walking in front of other people, if he is first arriving during Shemona Esrei, then you obviously are not davening together with everyone else, and if he gets there anytime before Shemona Esrei, there is no issue of walking in front of the other people, as this issue is only during Shemona Esrei.
As a side point if the bochur can hear every word of the chazan, he can also be yotza by hearing the chazan.