Is the aforementioned hadith from the Messenger (peace be upon him) to Umar ibn al-Khattab, in which he commanded him to wash his private parts and perform ablution after a wet dream, authentic? And what are the simplest ways to perform ghusl to remove janabah (ritual impurity)?

It is permissible to delay the ghusl (ritual bath) for janabah (state of ritual impurity following sexual intercourse or seminal discharge) until the time of standing for prayer, even if there is no necessity, because it is an obligation that can be postponed. It is permissible for a person in a state of janabah to sleep before performing ghusl, and it is recommended for them to perform wudu' (ablution) before sleeping. However, if a person in a state of janabah is unable to perform ghusl due to cold and the unavailability of means to heat water, they should perform tayammum (dry ablution) and pray. It is more cautious for them to repeat the prayer. If they do not find sufficient time for ghusl and fear that the prayer time will expire, the majority of scholars hold that they must perform ghusl even if the time expires.