Drawing the modulus from a Transfer function
Your sketch is not bad at all. I don't know why your teacher drew a "minimum" (do you mean a zero?) at $\pi/4$, because there shouldn't be any. The zeros are clearly at $\pm\pi/2$ and at $\pi$, and the main peak should indeed be close to $\pi/4$. By the way, I'm missing a pole. There are $4$ zeros and only $3$ poles. The fourth one should probably be at the origin. Maybe your teacher didn't give this exercise as much thought as he should have ...

EDIT:

Concerning your second example, it's always the same: a pole gives a bump in the magnitude response, the closer the pole to the unit circle, the more pronounced (sharp) is the bump. A zero on the unit circle gives an exact zero in the magnitude response, a zero away from the circle gives a dip. The closer the zero to the circle, the more pronounced (deeper) is the dip. Note that the exact maxima and minima in the magnitude response caused by poles and zeros close to the circle are often not exactly at the frequencies that correspond to the angles of the poles or zeros, but often they are close. This is all about a basic sketch, so no need to try to be overly precise.