How should we treat non-Muslim neighbours, family etc, especially those who are very kind, helpful, offer gifts and don’t show any hostility against Muslims or Islam? Also some of them have children outside marriage, may we give the children gifts or would this be showing that we accept their behaviour?
May Allah reward you abundantly ameen
You treat them with good manners but without liking them in your heart. You can give them gifts in return to theirs but not on their non-Muslim occasions. Yes, you can give gifts to their children. Put the intention of giving them dawah with your manners.