I am setting up my antenna. Is the antenna looking at the variation in the magnetic field? Should the normal to the plane of the antenna loop point perpendicular to the line-of-sight from the monitor to the transmitter?

Yes, basically sight down the plane of the antenna towards where the transmitter ought to be.

In practice if you can hear the signal on the receiver, you should get a sharp null when the loop is at right angles to the signal path. The null is a lot sharper than the peak. If you mark the antenna orientation for the deepest null, then rotate 90 degrees. Since the peak is broad in azimuth, your aim does not have to be very precise. But in direction-finding with loop antennas, you normally use the null rather than the peak. If you are working with students, you can demonstrate this principle with an old portable AM radio. Take the back off and show them the ferrite loop antenna inside. Point to a transmitting tower in view, and demonstrate that rotating the radio gives a peak and a null as the loop antenna rotates.