Is vigorous cleaning of the anus with water and repeated rubbing an indication that a light brown stain that appeared later came out after performing ghusl? And could this stain have come out with gas after Fajr prayer or during sleep? And is it necessary to repeat ghusl and prayer and make up for the fast?

Summary: It is recommended to seek refuge from obsessive whispers (waswas) and not pay attention to them. Your ghusl (definition) (ritual bath) and prayers are valid, and there is no need to repeat them. The general rule is that what has exited as impurity has already exited. Removing impurity is not a condition for the validity of wudu (ablution) and ghusl according to many scholars. Even if there was impurity, your prayer is valid due to your ignorance of its presence, and your fasting is valid in all cases. Trust in Allah is what brings benefit and repels harm. Sufficient istinja (definition) (cleansing after defecation or urination) is achieved when the area returns to its original texture. Overwhelming probability is sufficient for this; certainty is not required. There is no need to purify places or clothes unless you are certain of their impurity.