My question is can it run these if I purchase a 9v adapter? Or is the only solution to power one of them from a battery pack?
Plugging a 9vdc wall wart adapter into the external power connector of your Arduino may not solve your problem at all. The USB power is limited to 500ma by a fuse. Any external power used via the external power connector goes to a on-board +5vdc regulator. So if you still try and wire your servo and motor from the Arduino +5vdc the current will be limited to the on-board 5vdc regulators current limit, which may be a little higher the USB 500ma, but not a lot more.
Any time you need to power external devices that require larger amounts of current in excess of the Arduinos +5vdc current limit, is best done with suitable external power supplies wired directly to the devices. You need to be sure what voltages those devices require and if they need regulated voltage or not, and of course how much current the devices require.
There is no simple answer, only specific needs for specific devices. One needs to know the voltage and maximum current requirements for all external devices before the best power management solution can be determined.