Is the person who performed 'Umrah while in a state of ritual impurity (junub) due to ignorance—despite having exited the state of ihram—still considered to be in a state of ihram? And is a sacrifice (dam) incumbent upon him, or if he is unable, then feeding the poor?

If you performed ghusl (ritual bath) with the intention of the Sunnah bath for Ihram, then your ghusl removes janabah (major ritual impurity), and your tawaf (circumambulation) is valid. However, if you did not intend the Sunnah bath, then your tawaf while in a state of janabah is invalid according to the majority of scholars, and your Umrah is incomplete. You must then exit your state of Ihram by slaughtering a sacrificial animal (hady) and shaving or shortening your hair, or by fasting ten days if you are unable to provide the hady. This is unless you stipulated at the time of Ihram that your place of exit is where you are detained, in which case you exit by intention without hady or fasting. Some jurists hold that purity for tawaf is an obligation, not a condition, meaning your tawaf is valid, though repetition or expiation (fidyah) is required according to the Hanafis. This opinion is permissible when it is difficult to act upon the opinion of the majority.