The type of modulation is double sideband suppressed carrier. On positive portion of the modulating signal the carrier is in phase with the supplied carrier. On negative portions of the modulating signal the carrier is inverted. This is illustrated in most good explanations of sideband transmission.
Now for the sidebands and bandwidth required......
A square wave is a mixture, or a sum of the amplitude of several of sine waves. A square wave of any particular amplitude contains a sum of the odd harmonics of the frequency of the square wave. It contains 1X amplitude of the fundamental square wave frequency plus 1/3 of the third harmonic plus 1/5 of the fifth harmonic, 1/7 of the seventh harmonic, etc, etc, ad infinitum. Yes it indeed requires infinite bandwidth. Every harmonic modulates the carrier and produces sum and difference frequencies to be transmitted. If your bandwidth is limited, harmonics will be missing from the demodulated signal. The demodulated waveform will be less "square". The rising edges of the demodulated square wave will be less sudden. They will be sloped, and the square wave will have slight ripples due to missing harmonics.
The phase of the harmonics of a square wave is such that they must all have a zero crossing point from negative to positive at the same instant in time that the fundamental crosses zero from negative to positive. You can imagine how with every missing harmonic, the leading edge of the quare wave becomes a little less square and a little more sloped.
This pertains to 50% duty cycle square waves. If the modulation is not 50%, the the products will also contain even order harmonics.
If the modulation is just a single transition of DC, then its like ringing every bell in sight with a single blow.
I hope this helps.
