What is the ruling concerning prayers previously performed while there was a brown trace in the cracks of the foot, which is possibly a barrier, and must these prayers be repeated?

The fundamental principle is the obligation to remove any barrier between water and the skin during ablution (wudu') and ritual bath (ghusl), including dirt in the cracks of the foot. Ablution is not valid with the presence of a barrier, whether it is much or little, even if there is a view that pardons a small amount. However, it cannot be definitively stated that what the questioner mentions is a barrier preventing the validity of ablution, as usually a barrier does not remain for a long time with frequent ablution and foot friction.