In the neutral point topic , what is the orientation of the magnet?
The orientation of the magnet here with respect to earth's magnetic field is the magnet is perpendicular to the earth's magnetic field.
Why should the cross section of potentiometer wire be
uniform?
If the cross sectional area of potentiometer wire is not uniform , then potential gradient will not be same at all places on the potentiometer wire. Consequently, the measured value of potential difference will not be correct.