I mean, there are lots of ways to fake gold. At least one of these has some gold on the outside - which isn't going to simply wash off in the bathtub. And I'm guessing there are ways to make sure it sinks in water, as cheap and mid-grade jewelry tends to sink to the bottom too.
Yes, but that trick doesn't work so good when you use tungsten to fake gold, because they allmost got the same density. Thats also probably why the tungsten price recently went up together with the gold price, despite no significant increase in industrial demand for tungsten. Because thats how gold bars gets faked today.
It was a bit of a joke as you can use water displacement and weight to determine density.
If you’re buying a brick of gold you buy it from someone licensed to sell it (you usually have to be) and the regulations and verifications involved are pretty trustworthy.