What is the ruling on previous 'Umrahs that were marred by some errors or doubts, and how can expiation be made for them? And does the last correct 'Umrah supersede those that came before it?

There is no harm in a minor performing Umrah without a head covering, as the validity of Umrah does not depend on it. If ablution (wudu) is broken during tawaf and you complete it, you must repent and sacrifice a sheep. However, if it is broken after tawaf and you complete the sa'i without ritual purity, then nothing is required of you, as ritual purity is not a condition for sa'i. A man unintentionally touching your shoulder does not invalidate ablution, but you must avoid crowding men. A sin committed after Umrah requires repentance. Doubt concerning the number of tawaf circuits after its completion does not affect the validity of Umrah. Expiations (kaffarat) remain a responsibility until they are fulfilled.