Is a woman required to perform the Iqamah for prayer and the Adhan when praying alone in her home or with a group of women?

Neither the Adhan nor the Iqamah are obligatory or prescribed for women. This is because the assignment of the Adhan and Iqamah to women, or a woman undertaking them, was not known during the time of the Prophet (peace be upon him) or during the era of the Rightly Guided Caliphs.