Help interpreting strange spectrum
The multitude of spurious frequencies in your FF transform are reflections of undersampled higher harmonics of your signal. These are aliases, as you rightfully noted. See this EDN article for better explanations.

You are not using any cut-off filters on your signal, so all harmonics above the Nyquist frequency are "folded" back into the main frequency window. If you slightly move your main frequency, you will see that some peaks will move left, some move right, since they are coming from different folds.