What is the ruling on Umrah if the circumambulation (Tawaf) began after its prescribed start time, and what is the ruling on verbal altercations that occurred during Hajj as a result of anger and not suppressing rage during crowding?

If you performed all or part of the circumambulation (Tawaf) without intention (niyyah), there is a difference of opinion regarding its validity: it is valid according to the Shafi'is and Hanafis, but invalid according to the Hanbalis and some Malikis.

According to the view that the aforementioned Tawaf is invalid, you would have entered into the state of Ihram for Hajj after that for 'Umrah. The Tawaf you performed would suffice for Hajj, but you would owe a sacrifice (dam) for the combined pilgrimage (Qiran) and a sacrifice (dam) for the shortening (taqseer) that occurred in an improper place. The minimum sacrifice is a sheep to be slaughtered in the Haram and distributed to the poor. One can delegate someone to carry this out.

Quarrels and disputes during Hajj make the Hajj valid, but one must seek forgiveness and repent. It is essential to suppress anger and avoid wrath.