No, that's not how the scientific method works. It works by failing to disprove something, and continuing to fail to disprove it until you run out of ways to disprove it. Then you create a theory that explains the observation, and when a new way to disprove it comes up you try again and refine the theory based on whether you can or not.
Nor should science. It's only ever one disproof away from not being settled.
Only one correct kind, certainly. The principles behind a sunrise are objective, but people still have lots of beliefs around why it happens. They're wrong, but they still believe them.
No, I referred to logic, for a very specific reason. If one can use logic to create a conclusion based on a logical first principle, the conclusion is logical. If we can use logic to create a moral position based on a logical right, the morality is logical - and objective.