All those situations in the IVF method are impermissible in which the sperm of a man are entered into someone's uterus, other than wife, or the sperm and ovum of the husband and wife are developed in someone else's womb.
There is a Hadith in Sunan Abu Dawood:
Translation of Hadith: It is not permissible for anyone who believes in Allah Ta'ala and the Qiyamah that he should water someone else's field i.e. impregnate someone else apart from his own wife. (Sunan Abu Dawood, Kitab Un Nikah, Hadith No. 2160; Musnad Ahmed, Hadith No. 17453)
Safeguarding the ancestry and parentage is of great importance. This is what distinguishes human beings from animals.
For this reason, the Shariah has not permitted the woman to marry immediately after Khula, divorce, annulment of marriage or death of the husband. The Shariah has decreed Iddat (mandatory waiting period) so that if there was any conception from the previous husband, it should play itself out.
The man and woman between whom sexual relations are impermissible, combining their sperm and ovum is also not permissible, regardless of whether it is done in a lab or whether the sperm is directly introduced into the womb of the woman (artificial insemination).
The pure laws of Islam have declared eating/drinking the left-over of a non-Mahram (an unrelated woman with whom marriage is permissible) woman for the fear that the saliva of the woman will be mixed with the saliva of the man and the man may draw pleasure from this. The Shariah has declared the hair of the woman also to be Satar i.e. those body parts which must be covered, so that a non-Mahram man may not see them and draw pleasure from it. The law which has such meticulousness is these matters, how can it allow the sperm and ovum of two unrelated people to be mixed? It will be a severely indecent act and a grave sin.