Indeed, those lines should be freehanded using the ghosting method. As for how to draw a perfect square in perspective - not to spoil the big reveal, but that's precisely what that part of the challenge is about. The box challenge has its basic line extensions, and as we analyze our results and adjust our approach, we steadily improve on getting our lines to converge more consistently. The cylinder-in-boxes adds to those line extensions with those pertaining to the ellipses themselves (the minor axis, and the two from the contact points). Those additional lines will only converge to the box's VPs if that ellipse represents a circle in 3D space, which is only possible when the plane enclosing it is a square.

Therefore we iteratively improve our ability to estimate the proportions of our faces to be closer to squares as we perform the analysis and adjust our approach to better line up those line extensions.