I have some brief questions about the Salaam greeting:
1- If someone visits my home and says the Salaam but I do not want to accept him (for some reason), can I return the Salaam quietly?
2- If someone says the Salaam and he is far away (like by using sound system or mic) and no one answers him while even if I answer him, he will not hear it, what I should do?
3- Similar to 2, if someone is running or on a vehicle and says the Salaam to me while I am not able to answer him, what should I do?
4- If so many letters were sent to me and I just read them while they all contain the Salaam, do I have to reply them one by one? What if the sender was the same person?
5- With regards to 4, can I answer the written Salaam by whispering so as not to bother other people?
Thank you for your patience in answering me, and may Allah reward you with much good.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

Returning the Salaam greeting is an obligation by the consensus of scholars, and according to the majority of the scholars, it is recommended to be the one to start with it.

As for your first question, returning the Salaam quietly is not considered returning it in a way that clears you of your liability of this obligation. Al-‘Ayni wrote, “Returning the greeting is not valid until the person who greeted first hears it, unless he is deaf; in this case, the greeting is returned by moving the lips.” [‘Umdat Al-Qaari Sharh Saheeh Al-Bukhaari]

Therefore, you must return the Salaam in an audible voice so that the greeting person would hear it. The fact that you do not want to receive him in your house does not justify returning the greeting quietly and refraining from fulfilling the obligation in this regard.

As for your second and third questions, it is an obligation on you to return the Salaam to the one who greeted you with the Salaam from a distance, in fulfillment of the right of Allah, the Almighty, even if he sent the Salaam through a device or loudspeaker, if you had heard his greeting, because he greeted you and you heard it.

As for your fourth and fifth questions, if you receive letters containing multiple greetings, you are obliged to return the Salaam verbally and immediately every time you read a letter that has a greeting of Salaam. In Sharh Muslim, An-Nawawi commented on the hadeeth wherein the Messenger of Allah, sallallahu ‘alayhi wa sallam, said to ‘Aa'ishah, may Allah be pleased with her: “Jibreel (Gabriel) sends you the Salaam,” and she returned the Salaam, saying, “ and the mercy of Allah.” An-Nawawi said, “...It indicates that sending the Salaam is recommended ... and the one who receives the Salaam returns it. The scholars of our School (Shaafi'is) said: returning the Salaam is an immediate obligation. Likewise, if he receives the Salaam in writing, he is obliged to return it verbally as soon as he reads it.”

In this case, one does not have to raise his voice when returning the Salaam because the other person would not hear him.

For more benefit, please refer to fatwas 126280 and 308047.   

Allah knows best.