Is it permissible for a woman to go to the Haram alone and perform Tawaf by herself, as well as throw the pebbles (ramy al-jamarat) and perform Tawaf al-Ifadah within a mixed crowd without a Mahram?

It is permissible for a woman to go from the hotel to the Haram (definition) on foot and perform Tawaf (definition) without a Mahram (definition), as well as to go to stone the Jamarat (definition), provided she is safe and not adorned (tabarruj). The condition of a Mahram applies to travel, not within the city. When moving by taxi within the country, it is required that there is no khalwa (definition) (private seclusion) with the driver, which is negated by the presence of another woman with her. What is prohibited within the city is a man being in khalwa with a woman, unlike travel where a woman is prohibited from traveling without a Mahram.