Stepper motor shaft vibrating and vibrates the load
Only use full steps for max torque. Use appropriate pulley ratios on belt to increase torque as required.
motor noise while moving  is due to mechanical resonance, which is dependent on lack of stiffness and lack of damping and bearing slop exciting frame resonance.
Motor noise while idle should not occur but if you hear a squeal noise , it is because of electrical resonance , which depends on supply noise and cable characteristics which transfers motor inductance to the  driver.
Ensure at if 2A=24W that the motor has a miniature fan for cooling and same for electronics.
Your motor coil specs are 1.7A and 1.5 Ohms.