Answered by Sidi Moustafa Elqabbany
When I arrive late for a salat which is prayed aloud, how do I complete the rest of the rak`ahs- loudly or silently? For example, if I arrive in the second rak`ah of Maghrib or in the fourth rak`ah of `Isha, do I pray as if I was alone when the imam has finished and do I have to read a sura after al-Fatiha?
Most of your questions have been addressed in Shaykh Amjad’s answer below:
Joining a Prayer in the Third Rakah
It is never permissible to pray totally silently. Rather, the minimal audibility for the verbal integrals of prayer is that you should be able to hear yourself if you were in a silent room. You are not required to recite loudly enough to hear yourself in a room with background noise. All of the foregoing applies equally to men and women.
If you are a man praying alone or as an imam, the sunna is to recite loudly in the first two rak’ahs of Maghrib,` Isha’, and Fajr. The first rak’ah you pray is your first rak’ah, even if it is the imam’s last rak’ah. Reciting loudly means that a person standing next to you is able to hear you. Women do not recite loudly in the presence of marriageable men.
And Allah the Exalted knows best.
Note: this question was answered according to the Shafii school. The answer in the Hanafi school is essentially the same, though. Faraz Rabbani.