Can a Muslim be a sincere friend to a kaafir?
Question

                I have questions about Islam; can you explain them to me? Is it permissible for a Muslim to be a sincere friend to a person who is not Muslim?.
Praise be to Allah.It is not permissible for a Muslim to make friends with a mushrik or to take him as a close friend, because Islam calls on us to forsake the kaafirs and to 
    disavow them, because they worship someone other than Allaah. Allaah says 
    (interpretation of the meaning): 
“O you 
    who believe! Take not as friends the people who incurred the Wrath of Allaah 
    (i.e. the Jews). Surely, they have despaired of (receiving any good in) the 
    Hereafter, just as the disbelievers have despaired of those (buried) in 
    graves (that they will not be resurrected on the Day of Resurrection)”

    [al-Mumtahanah 60:13]
This was also the 
    teaching of the Prophet  (peace and blessings of Allaah be upon him). 
1 – It was 
    narrated from Abu Sa’eed al-Khudri (may Allaah be pleased with him) that he 
    heard the Messenger of Allaah  (peace and blessings of Allaah be upon 
    him) say, “Do not keep company with anyone but a believer and do not let 
    anyone eat your food but one who is pious.” (Narrated by al-Tirmidhi, 2395; 
    Abu Dawood, 4832. Abu ‘Eesa al-Tirmidhi said: this hadeeth is hasan. It was 
    also classed as hasan by al-Albaani in Saheeh al-Tirmidhi, 2519). 
Abu ‘Eesa 
    al-Khattaabi said: Rather he warned against keeping company with anyone who 
    is not pious and against mixing with them or eating with them, because 
    eating with a person instills friendship and love in the heart. 
He said: do 
    not make friends with anyone who is not pious; do not take him as a 
    companion with whom you eat and chat. 
(Ma’aalim 
    al-Sunan, Haamish Mukhtasar Sunan Abi Dawood, 7/185, 186). 
2 – It was 
    narrated from Samurah that the Prophet  (peace and blessings of Allaah 
    be upon him) said: “Do not live among the mushrikeen and do not mix with 
    them, for whoever lives among them or mixes with them is not one of us.” 
    (Narrated by al-Bayhaqi, 9/142; al-Haakim, 2/154. He said, it is saheeh 
    according to the conditions of al-Bukhaari. The hadeeth was also classed as 
    saheeh by al-Albaani in al-Silsilat al-Saheehah, 2/229 with its 
    corroborating reports). 
But it is 
    permissible to deal with them in a kind manner in the hope that they might 
    become Muslim. 
It was 
    narrated that Anas (may Allaah be pleased with him) said: There was a Jewish 
    boy who used to serve the Prophet  (peace and blessings of Allaah be 
    upon him), and he fell sick. The Prophet  (peace and blessings of Allaah 
    be upon him) came to visit him. He sat by his head and said, “Become 
    Muslim.” (The boy) looked at his father who was with him, and he (the 
    father) said, “Obey Abu’l-Qaasim  (peace and blessings of Allaah be upon 
    him).” So he became Muslim, and the Prophet  (peace and blessings of 
    Allaah be upon him) went out, saying, “Praise be to Allaah Who has saved him from the Fire” (Narrated by al-Bukhaari, 1290).
 And Allaah knows best.