1. Washing the parts of the body in order and consecutively when doing Ghusl is not obligatory according to the majority of jurists. 2. The more correct scholarly view is that rinsing the mouth and nose is obligatory in both Wudu and Ghusl. 3. If a man or woman does Ghusl to remove major impurity, this Ghusl counts for Wudu too. 4. Wudu and Ghusl are valid even if any bits of food remain between the teeth, but removing them is better.

If the mascara does not prevent water from reaching the hair, then Wudu is valid. If it prevents water from reaching the hair, then it must be removed before doing Wudu or Ghusl.

You should remove the lipstick before you do Wudu, so that there will be nothing left that could prevent the water from reaching the skin, but if the colour or a trace of grease is left, that does not matter.