Those are the eternal questions, aren't they? Every culture has come up with different answers. Every individual must answer to his own conscience. But there are some universals...probably because behavior has a genetic base. All animal species exhibit common traits throughout their range - even if that range is very, very large.
The problem is that if you try to leave the answers to cultures and individual consciences, instead of trying to discover the answers which are simply right, there are individuals who believe the answer is, "Best for me, according to my pleasures." These people exist in all cultures. (Not to mention various cultural practices.) Are they wrong? If so, how do you know? If not, how can you claim to have explained morality in any sense, with or without the supernatural?