What is the ruling on a woman who performed Umrah while she was menstruating, and does she have to pay for prohibitions that occurred between the two Umrahs, and is it permissible to appoint someone to perform it on her behalf, and is it permissible to make up that Umrah, and does masturbation invalidate Umrah?

Your second 'Umrah served in place of the first, and through it you became disengaged from your first state of ihram. The transgressions you committed, which are among the prohibitions of ihram, do not invalidate it, and nothing is required of you due to your ignorance of the ruling. However, the more cautious approach – according to the majority of scholars – is that for actions involving damage (such as cutting hair and nails), you are required to offer the expiation of choice: feeding six needy persons, or fasting three days, or sacrificing a sheep. You may appoint someone to feed or sacrifice on your behalf in the Haram.