To this Brit: "Who's that woman?" is perfectly natural. However, through my childhood I had it drummed into me that referring to people in such a manner was rude.
"Is that man the postman?" I said at age 4 to my mother, pointing at a person walking down the road that I thought I knew.
"Rude!" she scolded me, without explaining why. Suddenly the rules of communication had changed without warning. Many natural and easy constructions were forbidden, including "She did it," pointing to Grannie who had performed some mundane task for me that I lacked the dexterity to do for myself.
I grew to learn later in life that such rules and regulations are worthless lumber whose sole purpose is to inform the rest of the world that one is of greater social importance than people who don't use pointless linguistic circumlocutions rather than straightforward communication.
So, feel free to use "Who's that woman?" and "She did it," at will, understanding that the only people you may offend are snobbish middle-class social climbers.