Is the wife obligated to repeat her first 'Umrah and offer a ransom to the poor of Makkah, knowing that she circumambulated six rounds and did not pray two rak'ahs after the circumambulation in her first 'Umrah?

The two rak'ahs of circumambulation (Tawaf) are a Sunnah according to the majority of scholars, so whoever omits them, their 'Umrah is valid. As for the circumambulation itself, if someone performs only six circuits, their 'Umrah is incomplete, and they must return to Mecca to complete it. If they return as a pilgrim, their most recent 'Umrah is a completion of the first one, and their entering into ihram for a subsequent 'Umrah is void because they are still in the state of the first ihram. It is also necessary to re-solemnize the marriage contract if it was concluded while they were in the state of ihram.