Would it be all right for me to ask for God’s forgiveness for a non Muslim though I know that God won’t forgive him due to his disbelief and false creed? Am I sinful if I prayed for him? Also can I read Quran and offer its reward for him in hope that God forgives him?

Ibn ‘Abass said that It is not permissible for anyone to judge on behalf of God on His creation and it is not allowed for anyone to decide who enters heaven or hell. There is a difference between the general ruling that the polytheist and the disbeliever are staying eternally in hellfire and between applying this general ruling on a specific person per se because this specific person could be pardoned due to his lack of knowledge about Islam which was not presented to him in an attractive way that could hold him accountable before God. Although a person can be a disbeliever according to the apparent state of not embracing Islam, we are not certain if he is pardoned due to his lack of knowledge or not. Therefore it is permissible for you to pray for him and your prayer is not considered as a sin or disbelief because we simply don’t know his ultimate destiny. The mere fact of knowing that someone died as a non Muslim, does not necessarily make him enter hellfire eternally or make us believe that God will never forgive him. There is a difference between the general ruling for disbelievers who will stay eternally in hellfire and between each and every individual case as we don’t know if the message of Islam reached him/her clearly in a way which hold them accountable in God’s sight. The ultimate destiny of people is solely known and determined by God Almighty.