Are sandals considered impure upon entering the bathroom if a brother urinates standing, and is what falls on the bathroom floor away from the toilet considered impure in this case?

You must turn away from obsessive thoughts and ignore them. The default state of things is purity, including the floor of the restroom and shoes, unless their impurity is certain. If a spot becomes impure with urine, it is purified by pouring water over it. It is recommended to designate specific shoes for the restroom to avoid obsessive thoughts. If a towel falls on the restroom floor, it does not become impure unless it falls on a spot wet with impurity, or if it was wet and fell on a spot where impurity is certain. Doubt alone does not render pure things impure.