It is permissible to recite the Salawat during the prayers and after it. The prayer ends with Tasleem, and anything can be done after it. However, it is recommended to recite Takbeer three times immediately after Tasleem.
Based on compulsory precaution, it is not permissible to donate an egg and fertilize it using a sperm from a man without a religious marriage contract between him and the owner of the egg.
It is not permissible also based on compulsory precaution to donate a fertilized egg. If this occurs, the embryo belongs to the man that donated the sperm and the woman that donated the egg.