Question: Is it permissible to have a baby by means of in vitro fertilization?
A couple who cannot have a child normally should make du'a to Allahu ta'ala through the wasila [intermediary] of Silsila-i Aliyya [a chain of notable Islamic scholars] and employ all permitted means. In vitro fertilization is permissible on condition that the sperm and ovum are taken from a married couple and no haram is committed during the process. (İslam Ahlakı)
It is not permissible to have a male doctor perform in vitro fertilization because having a child is not an extreme necessity, and it is possible to find a female doctor.
Question: Is surrogate motherhood permissible in Islam?
No, it is not permissible. It is written in the book Seadet-i Ebediyye, "Taking sperm from a man and, in a tube or something else, implanting it in the womb of a woman who is not married to the donor in order for it to grow into a baby is haram. The resultant baby will be considered an illegitimate child."
Question: Is there anything wrong with prenatal sex determination or in vitro fertilization?
No, these methods are not objectionable, but one must avoid committing sins while one is undergoing them.