simulate this circuit – Schematic created using CircuitLab
- First-order guess is that the motor is a series-wound "universal" (AC/DC).
- You can't tell just by looking at the motor. You need to look at the entire appliance and whatever additional circuit is connected between the motor and the mains power source.
- It is unlikely that motor will work on 6-12V (or even 24V, or maybe even 48V) But no way to be sure without knowing the ENTIRE picture (the rest of the circuit).
- The blue component is likely a capacitor (or resistor/capacitor) "snubbing" component. It suppresses arcing across the switch. The small black component is a diode with is probably used as a very crude way of reducing the power into the motor to implement a slower speed.
This is just a guess at what the circuit might be.
You did not reveal anything about your project or why you think this rather low-power but high-speed motor may be suitable?