Air conditioner with inverter technology

The inverter reduces the inrush current from the compressor, but it doesn't necessarily eliminate it completely. The voltage dip that occurs during starting will be less, however that depends not only on the inrush current but also on the branch circuit wiring, voltage drop, etc. In general you will see an improvement.

The main purpose for the inverter is to vary the compressor speed to match the load requirements, which minimizes the number of starts and stops, and also improves energy consumption. The nameplate data reflects steady-state operation, not transient values.

Maybe is doesn't but it nearly could.

The power requirement usualy increase with motor speed. Thus a controller could be designed with essentially NO initial surge and, perhaps, only a slight surge when the system shifts from inverter drive to direct drive as the systems is up to full speed.

It doesn't shift from inverter to direct drive, there's no reason for it. A VFD rectifies and filters the incoming AC to feed DC rails which are then used to power the output stage which gives you 3 phase AC at anywhere from a few Hz up to 80Hz or so. Most of the units I've seen do a soft start, but I've only dealt with them on machine tools, not AC compressors.

There is a load on the compressor motor as it tries to start, so the exact amount of starting current will depend on the design of the system. In theory it can be zero, but in practice in may not completely soft start. It certainly will be reduced. Full speed will still be on the inverter, at 60Hz and full voltage.

The induction motors in aircon/fridge/freezer compressors don't have much starting torque, although the locked rotor current can be high. They usually don't have enough starting torque to overcome any existing pressure differential across the compressor, so they typically either have a timer to ensure they can't restart too soon before the pressure differential has decayed away, and/or they have an auto reset current thermal trip to detect more than a few seconds of locked rotor current, and backoff for a timeout before retrying.