Duties of Muslims Towards Non-Muslims
Question

What is the duty of a Muslim towards a non-Muslim, whether he is a Dhimmi in a Muslim country or in his own country, and the Muslim is living in the land of that non-Muslim? 
The duty I would like to have clarified is interactions of all kinds, starting with greeting and ending with celebrating the non-Muslim’s festivals with him. Is it permissible to take him as a friend at work only? Please advise us, may Allah reward you.
Praise be to Allah.Duties of Muslims towards non-Muslims
Shaykh ‘Abd Al-‘Aziz ibn Baz (may Allah have mercy on him) said: 
“The duty of the Muslim towards a non-Muslim includes a number of things: 

Da`wah or calling him to Allah , may He be Glorified and Exalted. He should explain to him the reality of Islam when possible, with regard to whatever issues the Muslim has knowledge about, because this is the greatest kindness one can give to his fellow-citizens and to those whom he meets of Jews, Christians and others who may be polytheists. 

The Prophet (blessings and peace of Allah be upon him) said: “The one who guides others to goodness will have a reward like that of the one who does it.” 
He (blessings and peace of Allah be upon him) also said to `Ali (may Allah be pleased with him), when he sent him to Khaybar and instructed him to call the Jews to Islam: “By Allah, if Allah were to guide one man through you, that would be better for you than having red camels (the best kind).” Furthermore, he (blessings and peace of Allah be upon him) said: “Whoever calls others to right guidance will have a reward like that of those who follow him, without that detracting from their reward in the slightest.”
So calling the non-Muslim to Islam, conveying Islam to him and being sincere towards him are among the best means of drawing close to Allah. 

The Muslim should not wrong the non-Muslim, with regard to his physical wellbeing, his wealth or his honour. If he is a Dhimmi (non-Muslim living under Muslim rule), Musta’man (one who is granted security in a Muslim land) or Mu`ahid (one with whose country the Muslims have a peace agreement), then he should give him his due rights, and not transgress against his wealth by stealing, betraying or deceiving, and he should not harm him physically by striking or killing him, because the fact that he is a Mu`ahid or Dhimmi, or Musta’man, means that he is protected by Shari‘ah. 
There is no reason why we should not interact with him, buying, selling, renting, hiring and so on. It is narrated in authentic reports that the Messenger of Allah (blessings and peace of Allah be upon him) bought from the disbelievers who were idol worshippers, and he bought from the Jews, and these are interactions. When he (blessings and peace of Allah be upon him) died, his shield was being held in pledge by a Jew for some food he had bought for his family (blessings and peace of Allah be upon him). 
With regard to greeting, a Muslim should not initiate the greeting , but he may respond if greeted, because the Prophet (blessings and peace of Allah be upon him) said: “Do not initiate the greeting of Salam with the Jews or Christians.” And he (blessings and peace of Allah be upon him) said: “If the people of the Book greet you with Salam (by saying Al-salamu ‘alaykum), say ‘Wa ‘alaykum.’” So the Muslim should not initiate the greeting to a disbeliever, but if the disbeliever initiates it, and the Jew or Christians etc. greets you with Salam, then you should say “wa ‘alaykum,” as the Prophet (blessings and peace of Allah be upon him) said. 

These are some of the rights between a Muslim and a disbeliever. 
Another right is to be a good neighbour. So if he is a neighbour, be kind to him and do not annoy him; give charity to him if he is poor, give him gifts, give him beneficial advice, because these are things that will attract him to Islam and to become Muslim; and because the neighbour has rights.
The Messenger (blessings and peace of Allah be upon him) said: “Jibril kept urging me to be kind to my neighbour until I thought that he would make him my heir.” (Al-Bukhari and Muslim)
If the neighbour is a disbeliever, he still has the rights of a neighbour; if he is both a relative and a disbeliever, then he has two rights: the right as a neighbour and the right as a relative. 
One of the rights of the neighbour is that you should give him charity , but not Zakah, if he is poor, because Allah says (interpretation of the meaning): “Allah does not forbid you to deal justly and kindly with those who fought not against you on account of religion nor drove you out of your homes. Verily, Allah loves those who deal with equity.” [Al-Mumtahanah 60:8] 
According to an authentic Hadith narrated from Asma’ bint Abu Bakr (may Allah be pleased with her), her mother, who was a disbeliever, entered upon her during the truce between the Prophet (blessings and peace of Allah be upon him) and the people of Makkah, seeking her help. Asma’ (may Allah be pleased with her) asked the Prophet (blessings and peace of Allah be upon him) for permission - should she uphold ties of kinship with her? The Prophet (blessings and peace of Allah be upon him) said: “Uphold ties of kinship with her.” 
Can Muslims celebrate non-Muslim festivals?
With regard to celebrating non-Muslim festivals, the Muslim should not take part in celebrating their festivals , but there is nothing wrong with offering them condolences if a loved one dies, such as saying “May Allah compensate you in your loss” and other kind words. However, he should not say “May Allah forgive him” or “May Allah have mercy on him” if the deceased was a disbeliever, and he should not pray for the deceased if he was a disbeliever. He may pray for the one who is alive to be guided and to be compensated and so on.” (Fatawa Noor ‘ala Ad-Darb, 1/289-291).
And Allah knows best.