1) The speed of the stepper is controlled bij the stepperdriver.
2) The max speed of the axis depends on the voltage of your power supply, the step of your screw and the quality of your build (linear rails, allignment,....)
3) Pulleys are mostly for increasing torque and/or precision But you can connect the motor directly to the screw without problems.
Youtube: i don't think he uses steppermotors, i think he uses servomotors. With servomotors you can achieve more speed and acceleration but they are more expensive.