There is no set guidance in this regard. The only requirement is to achieve purity and to stay clean. The manner in which one achieves this has been left to the society in general and people have a good innate compass through which they can distinguish pure from impure and how to achieve purity. You can wash them together in a single bucket because ultimately they’re going to be washed away and be cleaned. But if you’re still not comfortable with it, then you may use separate buckets or wash them in turns.

Same is the case with floor, it is upto you, based on your experience and level of satisfaction whether moping achieves the purity according to you or washing of the floor. As a principle, no objection can be raised on either of them as long as they’re achieving the desired objective.