"So does this mean that this pre-amp will work best with low impedance headphones like the Grado headphones (32 ohms)?"
No
"What happens if I use higher impedance headphones like the ones offered by Sennheiser or Beyerdynamics? Does it mean that I would need to raise the volume?"
Yes (some headphone amps don't have enough voltage available)
"Also, does impedance value affect sound quality?"
No.
No
"What happens if I use higher impedance headphones like the ones offered by Sennheiser or Beyerdynamics? Does it mean that I would need to raise the volume?"
Yes (some headphone amps don't have enough voltage available)
"Also, does impedance value affect sound quality?"
No.