Does "fast" quality of weapons have any impact when parrying with such a wepon? According to the information found in FAQ, it looks like this quality has no impact on defensive actions. Am I right? If so, I really wonder why the main gauche (weapon used definitely for defence purposes) is a fast weapon?

Yes, Parry is not an attack action (Fast doesn't apply on Parry Active Defense)

It's Fast because it is "Dagger based", and you still have the possibility to attack with it. Even if you have a better weapon in the main hand, you could be disarmed/wounded/grabed/unable to use main weapon somehow, or simply trying to surprise an opponent and stab with the Main Gauche.