Does the bathroom floor and basin become impure from urine drops or impure water from the hand that may fall on them?

Doubt about the transfer of impurity has no effect and should be disregarded. If the questioner is not certain about urine drops falling, the default assumption is that they did not exit, and thus the bathroom floor does not become impure. Similarly, the bathroom sink does not become impure merely by a hand contaminated with impurity passing over it, unless there is certainty that it touched a hand wet with impurity. Be warned against falling into obsessive doubts.