What is the ruling on interrupting the circumambulation (tawaf), which is a pillar of 'Umrah, due to the falling of the upper garment (rida') and the uncovering of part of the 'awrah, and does this affect the validity of continuity (muwalat) and building upon the tawaf in the Shafi'i school of thought?

Doubt concerning an act of worship after its completion does not have an effect according to the Shafi'is. Continuity (muwalat) in tawaf is, in their view, recommended, not obligatory. So, if tawaf is interrupted without an excuse and then resumed based on what was already completed, it is valid. One builds upon the point the circumambulator reached, not from the Black Stone. As for the intention for tawaf in Hajj and Umrah, the sounder opinion among the Shafi'is is that it is not a condition, because the intention for the ritual (nusuk) covers it.