Yes you can power the motors from the +9V supply if you use a transistor. You could use MOSTFETS, NPN or PNP transistors for this and the circuit diagram provided should work for just about any common one (NPN or MOSFET). If you want to try a mosfet you can pick up an MPF102 transistor from Radio Shack for about a buck a piece.
The diode in the schematic is reverse biased--meaning the cathode is tied to the +V. In this configuration it does not normally conduct; however, when the motor is turned off the inductor (motor) typically dumps a large voltage spike (can be several hundred volts) for a very brief period. The diode conducts during this spike and suppresses it.
PS if you are just staring a great book is "Getting Started in Electronics" by Forest Mims