What should I do about the prohibitions I committed due to my ignorance that the Umrah was invalid because I was in a state of major ritual impurity (janabah) while performing it, and is the Umrah valid in this case?

According to the opinion that purity is a condition for the validity of circumambulation (Tawaf), then the 'Umrah is not complete. If you are unable to return to Mecca, you must perform the 'Taha'llul al-Muhsar' (dissolution of ihram for one who is prevented). As for the transgressions of ihram prohibitions committed out of ignorance of the ruling: if they were of the nature of luxury or comfort, then there is no penalty for them. If they were of the nature of causing damage, such as shaving or clipping nails, then there is a fidyah (expiation) of fasting for three days, or feeding six needy persons, or sacrificing a sheep. Some scholars hold the view that purity is obligatory for Tawaf and can be compensated for by sacrificing an animal (dam), but it is not a condition for its validity. This is the view of the Hanafis, who state that Tawaf performed by one who is in a state of major ritual impurity (junub) is valid, but he must offer a camel (badanah) for Tawaf during Hajj, and a sheep for Tawaf during 'Umrah. We hope that this opinion offers some ease for you.