Can a woman delay the Fajr prayer until just before Dhuhr due to intercourse that occurred before Fajr to increase the chances of pregnancy, and the necessity of not performing ghusl immediately afterward? And is her prayer valid with semen remaining inside the uterus after performing ghusl?

It is permissible to delay ghusl (ritual bath) from major impurity (janabah) as long as the time for prayer has not arrived. However, once the prayer time commences, ghusl becomes obligatory, and the prayer must be performed, though it is commendable to hasten the ghusl. Delaying ghusl until after the time for Fajr prayer has passed is forbidden and considered a major sin, based on Allah's saying: "Indeed, prayer has been decreed upon the believers a timed ordinance." There is no excuse for delaying prayer beyond its prescribed time, except for what permits combining two prayers. As for Fajr, it is absolutely impermissible to delay it. A Muslim should be keen on performing prayer at its appointed time, and intercourse should occur early in the night to allow for ghusl and performing Fajr prayer before sunrise. If a Muslim performs ghusl from janabah, the retention of semen after ghusl does not invalidate it, because it is a single emission of semen that necessitated a single ghusl. Wudu (ablution) suffices if semen is discharged without desire after ghusl.