Returning greetings to kaafirs falls into three categories
Answer
Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on him) said:
If a kaafir greets a Muslim in a clear manner, and says, “Al-salaamu ‘alaykum (peace be upon you),” then one should say, “Wa ‘alayka al-salaam (and upon you be peace),” because Allaah says (interpretation of the meaning):
“When you are greeted with a greeting, greet in return with what is better than it, or (at least) return it equally”
[al-Nisa’ 4:86]
But if it is not clear, one should just say, “Wa ‘alayk (and also upon you).”
Similarly if his greeting is clear and he says, “Al-saam ‘alaykum (may death be upon you),” then one should say, “Wa ‘alayk (and also upon you).”
The three categories are as follows:
1 – If he clearly says, “Al-saam ‘alaykum (may death be upon you),” then one should reply, “Wa ‘alaykum (and also upon you).”
2 – If there is some doubt as to whether he said “al-saam (death)” or “al-salaam (peace),” then one should reply, “Wa ‘alaykum (and also upon you).”
3 – If he clearly says, “Al-salaamu ‘alaykum (peace be upon you),” then one should reply, “Wa ‘alaykum al-salaam (and upon you be peace),” because Allaah says (interpretation of the meaning):
“When you are greeted with a greeting, greet in return with what is better than it, or (at least) return it equally”
[al-Nisa’ 4:86]
Ibn al-Qayyim (may Allaah have mercy on him) said:
If the listener is certain that what he said to him was “Al-salaamu ‘alaykum (peace be upon you), and he does not have any doubts about that, should he say, “Wa ‘alayka al-salaam (and upon you be peace)” or should he limit it to “wa ‘alayk (and also upon you).” What is indicated by the evidence and the basic principles of sharee’ah is that one should respond, “Wa ‘alayka al-salaam (and upon you be peace)”, because this comes under the heading of fairness and justice, and Allaah enjoins justice and kindness. Allaah says (interpretation of the meaning):
“When you are greeted with a greeting, greet in return with what is better than it, or (at least) return it equally”
[al-Nisa’ 4:86]
So He recommends kindness and enjoins justice. This does not contradict any of the ahaadeeth which speak of this issue, because the Prophet (peace and blessings of Allaah be upon him) only enjoined limiting the response to “Wa ‘alaykum” for the reason mentioned above, which is that they used to play with the words in their greeting. Then Ibn al-Qayyim said: Even though the general meaning of the verse is applicable, this refers to the usual words of greeting, not when they are playing with the words. Allaah says (interpretation of the meaning):
“And when they come to you, they greet you with a greeting wherewith Allaah greets you not, and say within themselves: ‘Why should Allaah punish us not for what we say?’”
[al-Mujaadilah 58:8]
If this reason does not apply, and the kitaabi (Christian or Jew) says, ‘Al-salaamu ‘alaykum wa rahmat-Allaah (peace be upon you and the mercy of Allaah),” then it is only fair and just to respond in a similar manner.
Ahkaam Ahl al-Dhimmah, 200/1
In Saheeh al-Bukhaari it is narrated from Ibn ‘Umar (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “When the Jews greet you, they say, ‘Al-saam ‘alaykum (death be upon you),’ so say, ‘Wa ‘alayk (and also upon you).”
If he holds out his hand to shake hands with you, then hold out your hand too, but do not initiate the handshake.
With regard to serving a kaafir by giving him tea when he is sitting in a chair, this is makrooh, but there is nothing wrong with putting the cup on the table.