There are several pins on the power connector for a SATA hard drive. Why so many?
The main reason is to distribute current across multiple pins so as to keep within the allowable current for an individual pin. A “molex”-style pin can support more current than SATA edge pins so more are needed. Second, there is space for 12V, 5V, and 3.3V sources. Finally, two of the pins are dedicated to signaling purposes.
I am guessing that the motor and the controller all have different power needs. I hadn’t thought about that.
That was one of my guesses but I didn’t know what kind of signaling a power supply would do to a hard drive. (I am a curious guy but IANAEE.)
There’s no motor. The head actuator is magnetically driven.
Here’s the SATA specs: https://en.wikipedia.org/wiki/Serial_ATA
Of course there’s a motor, to make the disk spin.
Of course. I realized that a few hours after my post! 
My mind was on some other posts on Reddit where someone claimed the actuator had gears!