Elon, Three Questions [video]

Seeing Musk's announcement of his Grok 4, three questions:

(1) Is there a function from the plane to the real line that is 0 on the Mandelbrot set in the plane, strictly positive otherwise, and infinitely differentiable?

If so, then what function?

If not, then why not?

(2) In the Kuhn-Tucker conditions, are the Kuhn-Tucker and Zangwill constraint qualifications independent? For an answer, give a proof.

(3) Given a triangle ABC, using Euclidean construction, inscribe a square so that each corner of the square is on a side of the triangle.

I solved this one in the 10th grade.