What type of motor is this

That kind of encoder doesn't control a motor directly, its single purpose is to give you feedback on the position of the motor shaft. Regardless of the kind of motor you'll need to monitor the position of the motor using the encoder and then control it appropriately until it's in the required position.

The algorithm might be something like a PID controller or just something simple that moves the motor in the correct direction until the position is reached, possibly slowing it down as it approaches the desired position.

A likely problem attempting to use it directly with a Raspberry Pi is that the encoder outputs as shown in the datasheet will probably occur too quickly to deal with in a userland program and would likely need to use interrupts (ie kernel code) to operate reliably. I'd normally use a seperate microcontroller for such a task to read the encoder and control the motor in real-time and interface that back to the Pi using a SPI or serial interface.

While it would make an interesting project I can't think of any especially easy way to use the combination with a Raspberry Pi and it would probably be a challenging project if you haven't done much with motor control systems.

^{simulate this circuit – Schematic created using CircuitLab}

1. First-order guess is that the motor is a series-wound "universal" (AC/DC).
2. 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.
3. 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).
4. 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?