Powering a servo with 9V battery and other questions
Don't use a 9V battery to power your servos.  9V batteries have low capacity (won't last long.)
Don't use a 9V battery to power your servos.  9V batteries cannot really deliver the current needed to drive one servo, let alone 3.
Don't use a 9V battery to power your servos.  You say your servos are rated for 4.6 to 6 V.  9V is too much.
Don't use a 9V battery to power your servos.  Lowering the voltage throws away half of the little energy they contain.  
You can't just lower voltage with a series resistor or a voltage divider.  You have to use a regulator of some sort.  A linear regulator is wasteful.  A switching regulator is less wasteful (more efficient,) but a 9V battery is a poor choice in any case.




Obtain and use a battery holder for 4 AA batteries.  That gives you 6V.  Your servos will be fine with that.

Or, use a USB power supply that can deliver 1A.  Your servos will be happy with 5V, and 1A should be enough current to operate all three servos at once.

I'd advise against using the 5V from the Pi.  The servos could put enough noise on the power supply to cause the Pi to reset.

I suggest you work your way through a simple tutorial like this one before you get started writing your own software and building your gadget.

That tutorial shows you how to connect a servo to the Pi.  Here's the wiring diagram it gives:



Note that the servo is powered separately from the Pi, and that the grounds are tied together.

The only real connection between the Pi and the servo is a control signal.  The Pi doesn't touch the power to the servo.

The wiring diagram shows a resistor in the control line.  It isn't required.  You can leave it out if you don't have one.

Try out a tutorial, then look into pigpio.

Pigpio lets you use more than one servo on the Pi.

If you run into problems, ask a specific question about exactly whatever problem you encounter.