Question: Can someone walk into a bathroom bare footed when the ground is dry and clean? What about when its wet(mostly water)?
Answer: If you don't know for sure there is najis on the floor you may walk there barefooted. It is better to use slippers if it is wet, because this is cleaner.
Question: Is it true as fiqh rule that Certainty doesnt get affected by doubt? i.e u have to be 100% sure when u wash something that najis has landed on it.
Answer: If a substance is considered pure (not najis) in the religion, then it is not considered najis until one is sure that it has come in contact with a najis substance that made it so. One achieves this certainty by observing the contact, or by being told by a trustworthy muslim. This is indeed based on the rule "certainty does not cease by doubt."
... and Allah knows best.