The jurists agreed that it is best to wipe the entire head, but they differed as to whether doing so is obligatory or not. The Malikis and Hanbalis are of the view that it is obligatory to wipe the entire head. The Hanafis and Shafi`is are of the view that it is sufficient to wipe part of the head.

If the beard is light and the skin of the face beneath it can be seen, then it is obligatory to run one’s fingers through it and wash what is beneath it. However, if the beard is thick and the skin of the face beneath it cannot be seen, then it is not obligatory to wash what is beneath it, but it is recommended to run the fingers through it according to the majority of scholars.

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.

Before wudu, you should say Bismillah. After wudu, you can say this du`a, “Ashhadu an la ilaha ill-allah wahdahu la sharika lah, wa ashhadu anna Muhammadan ‘abduhu wa rasuluhu.” For more, see the detailed answer.