What is the ruling on a woman who entered into a state of Ihram for Umrah from Jeddah, and then her menstrual period began when she was at the Kaaba, so she completed the rituals of Umrah? And what are the consequences for her after she returns home, fifteen days later? Is she still in a state of Ihram, and can her husband not approach her? And is she required to offer a sacrifice?

You are bound by the ruling of ihram (definition) since you entered into it. Performing tawaf (definition) (circumambulation) during menstruation is not valid, nor is the sa'y (ritual walking) thereafter. And because your tawaf was not valid, you are still in ihram. You must avoid the prohibitions of ihram, return to Mecca to complete the tawaf, sa'y, and taqseer (shortening the hair). You must repent to Allah for performing tawaf during menstruation. It is forbidden for your husband to approach you with intercourse or its مقدمات (preliminaries).