The US is very responsible with keeping the dollar stable. You might try to disprove me by pointing out the US debt, but that actually is what is keeping the economy, and the dollar, stable. Other countries like China and various European countries have so much invested in the dollar, and in the case of China, their entire economy relies on the dollar since China's own currency is unstable. They would never invest like this if they didn't think it was going to stay stable.
Yes, the dollar-based economy is sustainable, because currencies have been used for large and small economies throughout history. As long as the United States uses sound fiscal policy and curbs inflation, operating with the dollar on a global level should be sustainable. On that scale, the dollar would likely be shielded from any kind of volatile swings caused by regional instability.
No. A global economy that is dollar-based will never have the ability to be sustainable. This type of economy would quite simply be too volatile for sustainability. The global economy, like all national economies, is cyclical; and strong economies can always assist weak economies. If we were to base economic advancement on one singular economy, we would never recover from the down cycle.