Transformers and Varying DC Current

No, only change in flux will induce the emf in a ckt. and that only feasible with AC that goes in opposite direction also. But in case of DC that produce flux with no change that never cause any emf in circuit. In case of DC square wave you change the magnitude of a wave from zero to max.

A DC square wave will have a very high value of dv/dt as compared to the pure sine wave. When it is striked to transformer, a high value of dv/dt would not be responded by it, as a result, the waves are bounced back to the supply side leading to overvoltages i.e. voltage spikes would be observed. so could lead to saturation of magnetic circuit eventually.