The formula you are looking for is; Amps = HP x 746/1.73 x Volts x %eff x pf.
350 x746/1.73 x 480 x .90 x .90 = 261100/672 = 389 amps. This amperage assumes that the efficiency of the motor is at 90% and the power factor of the motor is also at 90%.
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Yes, that's possible, but only for low-powered motor. You know that in order to start, the stator must be supplied with voltages that are shows shift phase between them, so the trick is to use a capacitor (since it shifts phase current) to simulate a 3-phase source. As indicated in the following picture: http://freecircuitdiagram.com/wp-content/uploads/2010/10/Enabling-3-Phase-Motor-Operates-with-Single-Phase-Supply.gif
Depends on the motor. If it is a synchronous motor it will run too fast.
yes,
Only one neutral conductor is typically in a 3 phase panel.
It will probably run but not correctly. Low voltage will cause the motor to draw less amps than it's designed to. It will not reach its rated RPMs and such slow operation may shorten its operating life.