Mayoral candidate Zohran Mamdani has built his political profile on a promise to transform the city’s housing landscape — arguing for rent freezes, tax reform and redistribution from “richer and whiter neighborhoods” to low-income, outer-borough communities. But the Democratic socialist could face scrutiny over the home history of his own family — specifically, his mother, award-winning filmmaker and Columbia University professor Mira Nair. Nair, best known for directing “Monsoon Wedding” and “The Namesake,” quietly owned a luxury loft in Manhattan’s West Chelsea neighborhood for over a decade, The Post has learned. She purchased the unit at 420 W. 25th St....