Confirmation on Diode in parallel with a Resistor
The voltage across R2 will be the supply voltage, as it is connected directly across the supply.  R1 and the LED will have no affect on the voltage across, or current through R2 (assuming the supply can provide sufficient current).

The voltage across R1 will be the supply voltage minus the forward voltage of the LED.  The presence of R2 will not affect the current through R1 and the LED.

If you add an LED in series with R2, both LEDs will light, even if they have different forward voltages.

If you connect a second LED in parallel with the one shown, only the one with the lower forward voltage will light.