Is ghusl necessary if a sexual image comes to mind and one feels something exit the penis, but finds no trace of it upon waking, and what is the ruling on the prayers performed before ghusl if it is obligatory?

The sensation of a fluid discharging after ablution (wudu') without verifying its presence is considered a whisper from Satan (waswasa) and does not necessitate repeating the ablution. Rather, one must disregard it and consider the ablution valid. However, if the discharge of fluid is verified due to thinking about sexual scenes, it is most likely madhy (pre-seminal fluid) which exits upon reflection or foreplay. This does not require a ghusl (ritual bath); rather, it is sufficient to purify the madhy from the clothes and body, and perform ablution. If one is ignorant of the nature of the wetness, whether it is semen or madhy, they have the choice of considering it semen and performing ghusl, or considering it madhy and sufficing with purifying whatever it touched and performing ablution. The prayers performed after purifying the fluid are valid. If they were performed before purification, they are valid according to some scholars if the worshiper was unaware of the presence of impurity.