How fast we can change direction of rotation of a stepper motor
We can't tell whether you can do this since we don't know what your capabilities are, obviously.

A stepper motor can be reversed, of course.  The question is how fast, considering how hard you are driving it and how much effective inertia an other forces are at its shaft.  A stepper motor has a maximum speed it can be run at for a given drive level and still stay in lock.  That speed goes down the higher the force it has to produce.  Reversing direction is not different than taking any other step, except that the speed and mass of whatever is connected to the motor will apply a apposing force, so the speed you can reverse at will be much lower than the normal operating speed.

This applies to any accelleration or decelleration.  Reversing isn't special just because it happens to change the sign of the speed.