Is it likeable for the woman who doesn`t come for Friday prayer to have the Friday bath(Friday Ghusl)?

Surgical removal of prostate causes a man to ejaculate directly in the bladder whenever he makes love. Is he obliged to perform Ghusl(Ritual bath) in this case and in case he had a wet dream as well, noting that he won`t see any trace of semen on his clothes or body?

A patient of advanced stage cancer is having difficulty in repeating Ghusl (Ritual bath). What is the ruling on that?

What is the Islamic ruling on dyeing one`s hair while ritually impure? Should one have a bath first to make sure that water reaches all of the hair?