A double-pole breaker with a "60" on each half will trip at 60 amps. The reason it's two connected breakers is to give the circuit 240V potential, by using two opposing AC phases. These do not "add up" to more current -- you're using them to double the voltage.
So if the heater requires 240V power at 120amps, you will need double-pole breakers that can provide a total of 120amps, e.g. 4 30A double-pole breakers as Tester101 suggested.
An electrician will be able to tell you if your service panel can accommodate this extra load -- it's a lot, but your 200A service might be adequate, depending on the normal load elsewhere in your home.
Sort of. It depends on your frame of reference.
If you're looking at the ungrounded (hot) conductor from each receptacle, you'll end up with a 240 volt circuit. Since it's a single circuit, it can't be out of phase with itself. If you hooked up an oscilloscope to the ungrounded (hot) conductor of each receptacle, you'd get a single 240 volt sine wave.
If you're looking at the two separate circuits (e.g. the ungrounded (hot) and grounded (neutral) conductor from each receptacle), then you'll end up with two 120 volt circuits 180° phase shifted from each other. If you hooked up the oscilloscope to the ungrounded (hot) conductor and grounded (neutral) conductors from each receptacle (4 leads instead of 2), you'd see two 120 volt sine waves 180° phase shifted from each other.
The two sine waves should look something like this.
![sine waves from single split phase transformer](https://i.stack.imgur.com/TAXWp.jpg)
Because the waves are phase shifted 180°, the electrical potential between the legs (at the peak) will be 240 volts. While the potential between either line and "neutral", will be 120 volts.
If the waves were not phase shifted, they'd be at the same potential (or have 0 volts between them).
![in phase sine waves](https://i.stack.imgur.com/LfLhb.jpg)
So while this is not a multi phase system, it's also not a simple single phase system. Technically it's known as a "Single split phase system".
All of this; of course, assumes that the ungrounded (hot) conductors are from different legs of the service.
Best Answer
It's written really poorly, so it's neither true nor false.
In most modern panels, breakers that are directly next to each other horizontally are on the same leg. Breakers directly above or below are on a different leg.