All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The in vitro fertilization (IVF) operation (procedure where the joining of egg and sperm takes place outside of the woman's body) is permissible in Islam when the need arises, as long as the sperm is from the husband and the egg from the wife. One form of a permissible IVF procedure in Islam is when the egg is fertilized by the husband's sperm outside the wife's body and then the embryo is implanted in the wife's womb. Another acceptable form is taking the sperm from the husband and injecting it into the womb of his wife. These are the only two Sharee'ah-approved forms of IVF that are permissible in Islam.
As for your wife's prayer after performing dry ablution or while sitting down or lying on a bed, there is no harm in this if trustworthy doctors decided that performing ablution or standing during prayer would negatively affect her. Dry ablution is prescribed in the case of a lack of water or the inability to use it in performing ablution. Similarly, performing prayer while sitting down (or lying on one's side) is prescribed in case of a genuine inability to pray while standing. The due condition in such a case is the utter inability to perform prayer while standing. If your wife can perform ablution while sitting down or have another woman or one of her Mahram (individual of a prohibited degree of kinship) to help her perform the ablution, she is obliged to do so and dry ablution will not be acceptable in such a case.
Moreover, if she able to stand during the prayer, she is obliged to do so. The Prophet, sallallaahu ‘alayhi wa sallam, said: "Pray while standing and if you cannot, pray while sitting and if you cannot do even that, then pray while lying on your side." [Al-Bukhari]
If she is unable to pray while standing, she may perform the prayer while lying down on her side. If she cannot, she may perform it while lying down on her back with the soles of her feet directed towards the Qiblah (prayer direction) and her head should be slightly raised.
Allaah Knows best.