Hair straightener resistance
The resistor and the diode are just there to supply the indicator LED. LEDs require a series resistor to limit the current, and they don't like high reverse voltage, so the diode blocks that. The LED will flicker at 50Hz and if you swing the hair straighter around a bit you should easily see the flickering causing the light to break up.  

So the LED circuit has the diode, LED, and dropping resistor across the switched mains. The LED will see an average current of around \$ I_{av} = \frac {230V \times \sqrt{2}} {\pi \times R}\$. If it is 82K, not 82 ohms(!), then the average current would be 1.26mA, which is reasonable, and the resistor would dissipate about 1/3W. 

The PTC heaters are simply connected in parallel, one for each side.