Depends upon the motor and its load. Some are less. Compressors tend to be a lot more. Check the nameplate on the AC. Look for "LRA".
Momentary dimming of lights on motor starting is quite normal. If it is a 120V motor, the lights on circuits on the opposite may brighten. Some lights are more sensitive to voltage fluctuations: lights partially dimmed are much more noticeable; full on incandescents are less noticeable.