Can a woman not in ihram wear niqab (touching face) during salah, inside or outside masjid al haram and during nafl tawaf, when non mahram men are around?

Answered according to Hanafi Fiqh by

It is compulsory for a woman not in Ihraam to wear the Niqaab wherever she
is – in the Haram or outside the Haram.

and Allah Ta’ala Knows Best

Mufti Ebrahim Desai