If we accept ethical relativism and we reject the possibility that there are scientific, metaphysical, or logical proofs for moral principles, there are still ways to resolve some moral disputes rationally. So the answer to question #2 is sometimes 'yes.' For example:

• Some disputes will be resolved if we discover more about the circumstances in which an action occurred. You and I may disagree about whether Bob stole Mary's bicycle. If I discover that she gave it to him, I will change my mind. More seriously, you and I may disagree on the morality of the death penalty. But if DNA analysis proves that a large number of innocent people are being executed, I may change my mind.
• Some disputes will be resolved if we use scientific methods to determine the consequences of an action. You and I may disagree about environmental policy. I may not have realized that dumping waste into a river was killing people in a nearby town. Once I know that, I may change my mind about the morality of the dumping.
• Some disputes will be resolved if we examine the arguments and I can convince you that you are being logically inconsistent. You may then change your moral evaluation of an action in order to be consistent.

I know that this sort of resolution isn't always possible. We have been arguing about the morality of abortion for decades and gotten nowhere.

But sometimes these methods work and they do not depend on discovering foundations of the sort I mentioned.