Do the feds have any legal obligation to keep a minimum amount of gold and/or silver? If not, is the US dollar backed by nothing? Is there an inventory of how much gold the gov actually has?
No.
The Dollar is only backed by our ability to create more of them. Its only “value” is the confidence that it will be accepted as a medium of exchange.
No.
The fed "claims" to have something like $350 billion dollars worth of gold. So, in a $7 Trillion dollar economy, the dollar certainly isn't back by gold.
The fed refuses to allow congress to inventory the so called stores of gold. Making it logical IMO that they have been playing fast and loose with the gold and how much is really there.
Virtually none of the gold at the New York Fed is owned by the U.S. About 98% of it is owned by foreign countries and the New York Fed keeps it for them. Most of the rest is owned by international organizations. During the Cold War a lot of European countries stored their gold in New York because there was the chance, however slim, of a Soviet invasion. Now that that is passed there is no reason to keep it off shore so to speak.