Does the US Mint sell fake gold coins/bullions?

No way would the mint make fake bullion coins to sell to the American public. First of all, it is very difficult to stamp out coins of such fine detail on tungsten without cracking it or making the combination of gold and tungsten come out with the exact density of gold in such a small volume. It is possible, but not worth the high cost of replicating it. Once exposed, the news would just catch on like wild fire. Imagine if you paid $2,000 for an American 1 oz. Eagle coin from the mint and find out it is fake !! You'd go immediately to CBS News and the whole scam would just collapse. There would be a huge FBI investigation and officials will be prosecuted for sure. Just not going to happen. It is so easy to detect a fake gold coin, all you need is a pair of calipers that costs $16.00 at Harbor Freight and a digital pocket gram scale and you can calculate if the density is correct. If you really doubt it, just melt down the coin in a small pottery kiln and look for the tungsten slug inside.

By the way, the American Eagle is 22 Kt. gold, but the American Buffalo Coin is 24Kt (solid gold).

However, tungsten bars are a different story. If you have enough money to buy a gold bar from the Federal Reserve at a cost of about $500,000 per bar, I think you'd have enough money to have it professionally assayed before you accept delivery. They have electronic measurement equipment that can detect it by passing current through the bar now that only takes a few seconds to test bars. Not a problem.