Is wiping over the hair a condition for the validity of Wudu', and does hair dye constitute a barrier preventing water from reaching the surface of the hair or the root of its growth?

The original principle regarding hair dye is that it is a color without substance, so it does not invalidate ablution (wudu') nor does it prevent water from reaching the hair. However, if it has substance, like thick henna, then ablution is not valid unless it is removed. What is prescribed for wiping the head is to wipe only the outer part of the hair.

As for the method of wiping the head: you wet your hands, then place the tip of one of your index fingers on the tip of the other, and place them on the front of your head. Place your thumbs on your temples, then move your hands to the nape of your neck, and then return them to the place where you started.