Is it permissible for a menstruating woman to make the intention of Ihram with her family, and if she becomes pure, should she purify herself at her accommodation or at the Miqat of Al-Tan'im? Does she need to renew her intention again? Is it permissible for her to use personal hygiene products after purification if she entered Ihram while menstruating?

Menstruation and post-natal bleeding (nifas (definition)) do not prevent one from entering into a state of ihram (definition). Therefore, it is permissible to assume ihram for Umrah (definition), and it is recommended to stipulate a condition (ishtirat) at the time of assuming ihram. Do not circumambulate (perform tawaf (definition)) until you are pure. You do not need to renew your intention for ihram or go out to Tan'im. Rather, you should perform ghusl (definition) (ritual bath), then perform tawaf, sa'i, and shorten your hair. There is no harm in using shampoo and soap for a non-muhrim, provided it is not perfumed with what is considered a fragrance.