There is nothing wrong with dyeing the eyelashes with kohl or mascara or any other kind of dye, if it is free of harmful effects and the woman does not appear wearing it in front of non-mahram men.

There does not seem to be any reason why the eyelashes cannot be dyed black, because the basic principle is that it is permissible, and because that is similar to using kohl, and it is more appropriate to make the color of the eyelashes match the colour of the hair of the head.

But if the dye is something that prevents water from reaching the eyelashes, then it must be removed when doing wudu’.

However, one must continue to uphold the general guidelines of modesty that our religion has laid down, which includes not adorning oneself in a manner or with the intent to unduly attract the attention of the opposite gender.

As the Qur’an says, “And tell the believing women to lower their gaze and guard their private parts and not expose their adornment except that which appears thereof,” and it continues by saying, “let them not stamp their feet to make known what they conceal of their adornment.” (An-Nur 24:31)

Sperm is pure. It has been related by Muslim in his Sahih (hadith no. 288) from ‘Aishah (may Allah be pleased with her) who said: I remember scratching sperm from the garment of the Messenger of Allah (blessings and peace of Allah be upon) thoroughly, then he prayed in it. Her not washing of sperm and just scratching is an evidence that sperm is pure.

Based on this view, if a woman swallows sperm, it does require having a ritual bath. It is sufficient to clean her mouth by just washing it.

In Islam, it is unanimously held that all things are supposed to be deemed pure, and that it is not necessary that all what is declared forbidden is considered impure. This is because impurity is a legal ruling that needs evidence. For example, drugs and fatal poisons are forbidden, yet this by no means qualify them to be impure.

For this reason, some scholars including Rabi`ah, Al-Layth Ibn Sa`d, Al-Muzani (the companion of Ash-Shafi`i) and some other scholars hold that wine is pure regardless of its being unlawful, and that only drinking it is forbidden. However, the majority of jurists are of the view that wine is impure and forbidden.

Thus, we conclude that all that is impure is deemed forbidden, but not vice versa. This is because regarding something as impure is to forbid any physical contact with it, whereas regarding something as unlawful is not necessarily to forbid any contact with it. To illustrate, wearing gold and silk is unlawful (for men), yet they are considered pure by the consensus of scholars and thus can be touched by men.
If it makes a barrier between skin and water it must be removed. For extended eyelashes, it is not obligatory to wash them during wudu. Therefore, you can keep them.

Almighty Allah knows best.