Is Umrah acceptable if a woman performs its rituals while she is menstruating, with the exception of tawaf and prayer?

It would have been better if you had not entered into the state of ihram for Umrah if you strongly believed you would not be able to complete it before returning to your country. It was obligatory to learn the rulings of Umrah before embarking on it. Your Umrah is incomplete, and you remain in your state of ihram because the tawaf is a pillar, and you have not performed it. Your sai is invalid because it was performed before the tawaf. What is now obligatory upon you is to refrain from all that a person in ihram must refrain from, then go to Makkah, perform the tawaf and sai, and then exit the state of ihram. You are obligated to pay fidyah for every prohibited act of ihram that you committed knowingly. If you were ignorant, then nothing is required of you, except as a precautionary measure for destructive prohibitions. If sexual intercourse occurred while you were aware of its prohibition, your Umrah is invalidated, and you must complete it, sacrifice an animal (hady), and perform another Umrah in its place. If you were ignorant, then nothing is required of you. If you are unable to come to Makkah, your ruling is that of someone prevented (muhsar); you should sacrifice an animal (hady) and exit the state of ihram. If you are unable to do that, then you must fast for ten days.