For communications (servo pulses, stepper pulses, ultrasonic sensor pulses,) the Uno can do it just fine.
For power, no, you do not want to power motors or servos from the +5V of the Arduino, because it does not have enough amperage capacity. Hook the motor controller and servo VCC directly to your battery (meaning, your battery needs to be the proper voltage for your servo) or an UBEC.
Finally, stepper motors are not generally very good for propulsion, for various reasons. I'd recommend a regular gearmotor with an H-bridge to control it.