The input voltage on steppers seems strange because steppers contain inductive coils that we must switch on and off quickly. You know that an inductor tends to resist changes in current. If it has no current flowing through it then applying 3V to the 2 Ohm coil will make the current slowly rise up to 1.5A. But we want the current to get to 1.5A in a millisecond. So we can apply 12V for a millisecond and the current will rise to 1.5A much faster. Then the stepper controller must reduce the voltage to maintain 1.5A. The stepper controller must also switch the coil off quickly and the inductance will try to maintain the current flow. That requires active control to get the best performance.
You ask a lot of questions and I have to go to the airport in 10 minutes, so I'll make separate replies.