I refer to calculus of a single variable x. Standard Newton-Leibnitz developed calculus of a single real variable. In so far as your statement, “The differential of one variable with respect to another, the most basic concept of the calculus, demands at least two variables.”, that makes no sense. In single variable calculus, values of y are generally determined by the value of an input variable x. Thus y is not a variable itself but rather a function of a variable x.
Utter nonsense!