1.
What frequencies give rise to growing oscillations?

2. Why are these
frequencies effective?

any multiple of the
natural frequency so the drive will periodically act in the direction
of motion.

any fraction of the
natural frequency: net positive work only occurs when the force
switches and the force acts over a distance.

only odd fractions of
the natural frequency so that the drive spends more time acting in the
direction of motion (positive work) and less against it. (CORRECT)

A more mathematical response:
the oscillator is driven by the Fourier components of the square wave.