Breadboard Resistor/Motor Not working
You say that the motor draws 350 mA.  If you pass 350 mA through your 220 ohm resistor, Ohm's Law says there will be a 77 volt drop across the resistor - since you only have a 3 volt battery, this obviously won't work!

Ohm's Law indicates that 3 volts across 220 ohms will only result in a current of 13.6 mA.

Common LEDs typically have a maximum current of 20 - 30 mA, so they cannot be connected in series with your 350 mA motor - the LED would vanish in a puff of smoke!

If the motor is designed to operate on 3 volts, it should be connected directly to the 3 volt battery, with no series resistor.