Can we pray for non-Muslims? Please reply in the light of Quran and Hadeeth.

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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

It is not permissible to supplicate to Allaah to forgive or have mercy on a non-Muslim, or award him with any other reward in the Hereafter. Allaah Says (what means): {It is not for the Prophet and those who have believed to ask forgiveness for the polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire.}[Quran 9:113]. Imaam An-Nawawi said: 'It is forbidden by the text of the Quran and the consensus of the scholars to supplicate to Allaah to forgive a non-Muslim.'

As regards supplicating to Allaah to guide him to embrace Islam whilst he is alive, this is permissible. Indeed it is confirmed that the Prophet supplicated to Allaah to guide some non-Muslims as he said: "O Allaah guide the tribe of Daws and bring them forward to me as Muslims." [Al-Bukhari and Muslim]

However, it is not permissible to supplicate to Allaah to bestow on a non-Muslim worldly benefits if he is fighting against the Muslims, otherwise it would be permissible to supplicate for him to this effect.  

Allaah Knows best.