Define 'run out of'. The majority of gold that has ever been mined is still in existence in tangible form.
See above. Precious metals tend to not be used up but rather re-melted down and reused again over and over.
A likely scenario would be competing gold warehouses that issued receipts that could be encrypted and digitally transmitted through the Internet. From that, third party exchangers would emerge, and thus an entire currency ecosystem.
You don't. Arbitrage is an important mechanism to maintain a regular market. As it became more disaggregated it would create opportunities for people to push it back towards aggregation again. If gold (or anything else) became the common medium of exchange the opportunities for arbitrage would be tiny and fleeting.
Ha, that's nice. I like the idea of using gold as currency. That way the world will have one single currency. We all will live in a happy economy where there is no inflation globally, no politician in the world will ever come up with scheme to abuse the monetary system, and all country will have uniform monetary standard that meets all their economic needs.
World peace everyone!