Lots of incorrect information here.
Range mode does the following:
1. Puts HVAC into "economy" mode. It will use less energy, but will also not be as effective.
2. Allows the battery pack to get colder or warmer before using energy to raise/lower the temperature thereby conserving energy.
3. On P models, puts a torque bias to the front, more energy efficient motor.
4. At one point it turned off the DRLs on US MX cars. I think this changed via firmware at some point. I'm not sure. It was dumb anyway.
Depending on the ambient temperature, range mode will have almost no effect, to perhaps a 7% range boost (data on this has been all over the place.)
If you don't need the extra range, it's suggested you leave it off. The change in battery temp management comes at the expense of battery longevity and degradation.
Range mode has zero effect on charging speeds, with the exception of the roadster, which is a different animal.