Is it sufficient to wash only the area where the impurity is presumed to have fallen, or is it obligatory to wash the entire bathroom floor? And is washing it with a water-dampened cloth, so that the trace of water is visible from it, sufficient instead of pouring water?

If toilet water mixes with urine or feces, it becomes impure, and if it touches anything, that thing becomes impure. To purify a place affected by impurity, every spot that might have been touched by the impurity must be washed, especially if the exact location of the impurity is unknown. Wiping the impure spot with a wet towel is not sufficient; pouring water over it is necessary. It is advised not to open the door to obsessive doubts in such matters.