I believe one side of the cross-fade is off a NPN transistor, the other was PNP. The opamp fade only needs two, think he is either just using what he had handy, or showing that most any will work okay. I have used this circuit in several years, before I got into AVR microcontrollers. I wanted and RGB color fader, and used three of these. Still think it does a much better job, much wider range of colors, compared to the microcontroller and PWM...
To run of 12volts, think you need to adjust the voltage divider, probably better left to somebody who understands that stuff, not up on the math and theory.