"What make is it" usually refers to automobiles which have makes and models. Make being like a "Fiat" and model being "500". Make is not plural because it refers to a singular type of vehicle.

"Make" in that context isn't the same as it's usual use, e.g. "I am going to make some food" It typically refers to brand or who made a certain thing, such as "Those are really nice shoes, what make are they?" where the "Make" is the brand or company who made the item, e.g if the shoes are made by the company "Adidas" and have the Adidas logo on them, you'd say "They're Adidas"

Good question and good answers.