Is anything incumbent upon a woman who entered into a state of Ihram for Hajj or Umrah from Abyar Ali while she was menstruating, and then entered into Ihram again from Masjid Aishah (at At-Taneem) after she had purified herself? And if so, what is it and how is it to be fulfilled?

If a menstruating woman enters into a state of ihram from the miqat, her ihram is valid, and she should perform all the rituals that pilgrims do, except that she should not circumambulate the Kaaba until she becomes pure. There is no obligation upon her for delaying the ritual due to purity, based on the hadith of Asma bint Umays and Aisha (may Allah be pleased with them both). As for what the questioner did regarding the prohibitions of ihram out of ignorance after the initial ihram, there is no expiation required for it.