Mike Copeland wrote:

Motor starting surge is approx 3x the running current....plus an
inductive "kick" for a capacitor start(single phase) motor.

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.