What is the ruling on droplets of impure water splashing onto the legs and clothes while washing a menstrual blood stain, and does anything that subsequently touches the wet clothes become impure?

It appears you are afflicted with some form of waswasa (obsessive whispering/doubts). You must turn away from it and not give in to it. Do not rule something impure merely based on doubt. Since you have washed your leg from the impure water, you have fulfilled your duty. Your clothes are originally pure, as long as you are not certain that any of this water has touched them.