Gold only has a stable value when the government has a currency that they back. There are no examples of any material having a stable value in a place without currency.
Yes, the government did, as explained above.The US government had no hand in those systems whatsoever. The only reason the US dollar was legislated the only legal tender is because you had exchange rates from bank to bank and state to state which hindered trade (but did not stop anyone from generating wealth).
Market economies fall apart when the government has no debt, unless it is a heavily micro-managed economy.No, the literal root of fiat currency is debt. If the US government paid back every penny it owed to everyone out there, money would still be in circulation.