"This question wanted you to equate torque of ONE SIDE OF THE COIL ONLY!!"
What does that mean? How do we know? How could the question be worded so that it wasn't only on one side.
"It wanted to assume that the magnetic field lines had spread out."
What does this mean?
" Common errors included assuming the magnetic field was constant in the equation τ = nBIAcosθ"
Isn't it? What does this mean?
And if current is moving anti-clockwise in the coil, and the magnetic field direction is left, why is the weight on side X. Shouldn;t it be on side Y?
The question says that the mass is placed on side X OR side Y, meaning that it wants you to calculate the torque created by that mass. If the same mass was placed on the other side of the coil, then the torques created by both of the masses would cancel out, and you would have no rotational moment (due to mass on side Y creating a clockwise torque, and a mass on side X would produce an anti-clockwise torque)
Regardless if there is a north or south pole located on the other side, what you have to assume that the magnetic field lines are spread out, and are moving out of the north pole magnet. This means that you can assume that the magnetic field lines are travelling to the right.
The magnetic field is not constant, because the magnetic field lines passing through side X will be greater than side Y. What you would have to use is T = fd, where f is the force created by the mass (mg), and d is the perpendicular distance from the pivot to the point of rotation.
The reason why its not on side Y is because the magnetic field lines passing through that side is almost negligible, so you assume its on side X