It may be a good idea if the driver is appropriate for the motor. Post a motor data sheet. A4988 is good for around 1A coil current, so maybe.
Hard to say without knowing anything about the motor, driver, power supply or loading.
I have not seen a data sheet, so have no way of knowing for sure. Generally the supply voltage is the highest that the driver can safely handle for best speed. The driver controls current.
I don't see why not,but I have not seen your complete requirements. Or write your own code. It is not hard. See Robin2's simple stepper code tutorial.
I have not seen your complete requirements. How fast is fast? How much load? What positional precision?
Robin2's stepper motor basics may be of interest, too.