Regarding the question of egg donation, we would like to quote a fatwa issued by Sheikh Ahmad Kutty, an Islamic scholar in which he stated:
Egg donation is not allowed in Islam; this is because of the fact that it dilutes and mixes up blood lineages. In other words, it mixes the egg and sperm of two parties who are not married. In this way, it is no different from adultery.
There is a consensus among scholars on this issue. Hence, no Muslim should ever even entertain such an idea. Even If conception is only possible through this method, it is best for the parties to accept the will of Almighty Allah who says,
(Unto Allah belongs the kingdom of the heavens and the earth. He creates whatever He wills. He bestows female (offspring) upon whomever He wills, and bestows male (offspring) upon whomever He wills. Or He mingles them, males and females, and He makes barren whomever He wills. Indeed He is all-knowing, all-Powerful.) (Ash-Shura 42: 49-50).
In conclusion, let me state that in vitro fertilization is only permissible if the egg and sperm are extracted from a couple who are married to each other, and as long as a third party is not brought into the equation either as a donor or a carrier (otherwise known as a surrogate mother).