Does the fast become invalid if I have a wet dream and am affected in my sleep, even if there is no trace of the wet dream, and is Ghusl obligatory in this case?

Wet dreams during fasting do not invalidate it, because they are beyond one's control and cannot be prevented, whether or not semen is discharged. If accompanied by the discharge of semen, ghusl (ritual bath) becomes obligatory, based on the hadith of Umm Salamah in the Two Sahihs: "Yes, if she sees water." However, if it occurs without seminal discharge, ghusl is not obligatory. Therefore, your prayer and fasting are valid, and there is no sin upon you.