justone:
No need for it since the TIP120 already has a builtin kickback diode. See the datasheet.
No, that's wrong. The diode has to go across the inductor. You'l fry the TIP120 immediately if you
don't include a diode across the solenoid coil.
Since darlingtons drop 1.1 to 2V, a 5V solenoid needs 6 to 7V power supply to work with a darlington.
Use a logic level MOSFET and this isn't a problem, but you still need the diode.