1 & 2. My recommendation is a 1000W. But a good one. Corsair is a very good brand. Each 5970, not overclocked, will draw 300W on the +12V rails. Your CPU will never draw more than about 100W (that's a very liberal estimation). I suppose a corsair 850W would still work out fine. I recommend corsair because they are a quality brand with the power properly distributed to where it needs to be. If you are just going with one 5970, that takes off about 300W. You'd be fine with a 650W corsair.
3. Electricity does not work like that. The voltage is constant. The system will draw as much current as it needs. Voltage multiplier by current is equal to power. If your system has a 50,000W rated power supply but only needs 100W, then 100W will be drawn from the power supply. Note that I did not say from the wall. This is because the current drawn from the wall will be more because power supplies are not 100% efficient. In other words, assuming 80% efficiency, it will draw 100W/0.80=125W from the wall in order to provide the system with 100W. Maybe that's too much detail. The point is no matter how much power the PSU is rated for, it will only provide the amount of power needed by the system. The simple answer is "no."
On another note, I have often seen benchmarks where 3 5870s in triple crossfire beat, match or come very close to 2 5970s. If it is more cost-effective based on prices in your area, I would recommend it.