To answer the out of phase question, the AC power that comes into your American house (or at least all of the houses in which I have seen the breaker box) has, like you said, two live wires and one neutral/ground wire. The two live wires have 120VAC 60Hz on them relative to the neutral wire. Relative to each other, however, they would measure 240V on a multimeter. 120VAC voltage is always switching between +120V and -120V. The two wires being out of phase means that when one wire is at its positive peak (+120V), the other wire is at its negative peak (-120V). A multimeter connected to each of the live wires would measure the difference between them ((+120) - (-120)) = 240. This picture might help some. The red and yellow lines are what the voltage of each live line looks like over time.
Not sure if the microwave will be expecting two out of phase 120V inputs or just one 240V input.