2) A geometry textbook gives the equation of a parabola as y =x2, where x and y are measured in centimetres. How can this equation be dimensionally correct?

Answer 1

y = x^2 = x * x cm * cm or cm^2

So it is not correct.
It is probably a typo or they just mean that lengths are in centimeters, leaving you to figure out that area is therefore in square centimeters.