I very much doubt that faster charging is intrinsically more efficient. At the battery itself, faster is generally a bit less efficient. Separately, circuit details inside the charger could easily cause it to have different efficiency in the 110 and 220V modes, most commonly to the benefit of the later. Mrbigh already mentioned a difference in the PFC block of the charger.
Efficiency increases because energy loss decreases for the same amount of power. First, higher voltage circuits usually start off with thicker wires (less resistance). Second, P = I * V V = I * R, so P = I*I*R
You are confusing the insulation jacket with the conductor. For a given power, higher voltage circuits usually use thinner conductor, it doesn't make any economic sense to do otherwise. But the conductor is often not thinned at the same rate the voltage rises / current falls, so a portion of the I*I*R savings from your equations still gets realized.
No. Generally 240V charging is more efficient than 120V charging. You can confirm this by measuring the kWh consumed from a public charging station when connected to the L2 port versus the 120V outlet. The rate of charge being applied to the battery is well below the charge rate the battery chemistry can withstand. The charge rate from regeneration (braking) is much much higher than the charge rate applied from the onboard charger. The notable exception to the "generally" is when the ambient temperature exceeds the optimal temperature for charging. The PiP has limited capabilities for managing the battery temperature while plugged in and charging.
~240v should provide slightly better efficiency then ~120V. The gain is because a small amount of energy is wasted as electrical current heats the wiring from the electrical panel to the PIP. Lower voltage requires more current. Power factor is a different issue. And it is not a concern in residential power. The power utility would like to see a very constant load during each power cycle. In fact, many loads do not provide this perfect power factor. Some loads, like electric motors shift the load so peak current is drawn at a time slightly past the peak voltage. This phase shift costs the power utility to produce the electricity and it also takes larger generators and larger power distribution equipment to distribute power to a load with a poor power factor. Electronic power supplies are usually non-linear. The PIP battery charger is most likely a switched power supply. The front of that supply could simply be a rectifier, or a rectifier and a capacitor. If rectifier alone, the load on the power system will be pulses. If it includes a capacitor, it will draw current form the power grid at the peak of each AC half cycle. If it is utility friendly, it would load the power line taking pulses of energy all along the power cycle. Those pulses varying in position and duration to keep the load as close to perfect as possible. I wonder if the power utilities are working with the electric car manufacturers to provide power factor correction? And I wonder if the PIP already has it.
