Do residual toothpaste inside the lips, lipstick, foundation, and mascara that are not waterproof, constitute a barrier preventing water from reaching the skin, thereby necessitating redoing the ablution? And are small quantities of such barriers excused?

Mere color is not an impediment that prevents water from reaching the skin; rather, an impediment is that which has a physical mass. Creams and pastes, some of them have a physical mass and thus prevent water from reaching the skin, while others do not. A slight impediment is excused according to Shaykh al-Islam, and there is no harm in adopting this opinion for those afflicted with obsessive whispers (waswas). It is not obligatory to wash the inside of the lips when washing the face; rather, only what is visible should be washed. One must ignore obsessive whispers and turn away from them.