Assalaamu alaykum. 1) If someone greeted from a distance so that I could not hear his salaam (or what he said) clearly, is it obligatory upon me to reply to his salaam then? 2) Is it obligatory to reply with the salaam loudly so that the person to whom the reply is given may hear it?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

Returning the salaam (greeting) is obligatory; Allaah, The Exalted, says (what means): {And when you are greeted with a greeting, greet (in return) with one better than it or (at least) return it (in a like manner)...} [Quran 4:86]

An-Nawawi wrote, “Returning the greeting is obligatory according to the scholarly consensus...” [Al-Majmoo’]

Hence, whenever someone greets you by saying, “As-Salaamu ʻAlaykum” at a distance and you can still hear him, then it is incumbent on you to return the greeting; the clarity of his voice is not a condition for the obligation of returning the greeting; the condition is to hear his voice saying the salaam. This is enough to establish the act of Sunnah of initiating the salaam and entailing deeming it obligatory to respond to it.

The Kuwaiti Encyclopedia of Fiqh reads, “Statements of scholars almost collectively indicate that hearing the salaam is required for fulfilling the obligation of returning the salaam... An-Nawawi said in Al-Majmoo’, 'The scholars of our school of Fiqh held that it is required for the one greeting others or responding to their greetings to raise his voice so that the addressees hear it.'”

However, if you could not hear the salaam or heard unclear speech and you cannot be sure whether it was a salaam or not, then you are not obliged to respond because the scholars stipulated hearing the salaam to deem it obligatory to respond to it, as mentioned above.

Hence, the obligation of returning the salaam depends on hearing the voice of the person giving the salaam, even if at a distance.

Allaah knows best.