Is it obligatory to repeat prayers, and what is the ruling on touching objects after seeing sexual images in a dream without any wetness, then discovering a black spot and an odor upon waking?

If what you saw in your dream was sexual intercourse and you found wetness upon waking, then it is a wet dream (ihtilam) that necessitates ghusl (definition) (ritual bath), whether you know it to be semen or not. However, if you did not see intercourse and you are doubtful about the wetness, scholars have differed. Some have made ghusl obligatory, while others have considered it both madhy (pre-seminal fluid) and maniy (seminal fluid) out of caution. Still others have given a choice between considering it maniy, thereby necessitating ghusl and the re-performance of prayers, or not maniy, which would not require re-performance. As for the things that came into contact with it, they are pure, because semen is pure, and madhy does not defile something unless it is transferred to it with certainty.