Those 9v batteries are a very expensive and inefficient way to power an Arduino, but if the current requirements are low enough then it would be possible, if you insist.
Read the documentation for the Servo library for a clear explanation of what it does, but briefly:
The Servo library can control up to 12 servos (up to 48 on a Mega). The servos can be on any of the output pins (you are not limited to the pwm-capable pins). However, using the Servo library does disable some of the pwm output capabilities (which pwm-capable pins lose their pwm capability depends on how many servos you are using). Unfortunately, on all boards except the Mega using any servos disables the pwm capability of pins 9 and 10 which are the ones typically used to control the speed of a motor drive shield, so using servos and a standard motor drive shield can be problematic. If you used a Mega this wouldn't be a problem, and if you used a motor drive shield that didn't use pins 9 and 10 this wouldn't be a problem, and if you used a separate motor driver board connected by flying leads (rather than a shield) this wouldn't be a problem.