Is the questioner considered sinful for entering the Noble Rawdah and performing the rituals of Hajj (Tawaf al-Ifadah, Sa'i, visiting Madinah, and praying in the Rawdah) while brownish and coffee-colored discharge continued after her menstruation stopped, as she thought it was istihadah (prolonged non-menstrual vaginal bleeding)?

Brown discharge that appears after menstruation is not considered menstruation, but it does nullify ablution. If you performed ablution before circumambulating the Kaaba (Tawaf), then your Tawaf is valid. If you doubt whether the discharge appeared during Tawaf, the default is that your Tawaf is valid. However, if you are certain that it appeared during Tawaf or before it, and you did not perform ablution, then your Tawaf is invalid according to the majority of scholars. Nevertheless, a less preferred opinion might be given as a fatwa for those who do not consider purity a condition for the validity of Tawaf, as a facilitation. The more cautious approach is to offer a sacrifice (hady) in Mecca, as some scholars state that purity for Tawaf is obligatory and its omission can be compensated for by shedding blood. There is no sin in entering the Prophet's Mosque (Masjid an-Nabawi) because that discharge is not considered menstruation.