In order to start one's own economy, he must either barter goods and commodities or come up with his own fiat currency. Otherwise he is merely joining another economy. However, it could be argued that any new currency or system that joins the world is merely joining the existing economy as well. I suppose that in order to actually start ones own economy, one must start that economy on a deserted island so to speak. Or a deserted planet. Nothing can be traded or used with or against anyone else's economy or it merely joins that economy.
Yes, that's possible. Some towns have tried this. They printed their own currency, which was accepted in the local shops and received by the people for services. Just like the real money, but on a local level. Of course the governments (Germany and Austria I think) were not very happy about it and prohibited those activities. Especially after it showed that it actually works and the people profit from it, because it keeps the banks out and there is no tax money drained out from it.