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I have no idea whether there are any regulations in the US regarding this, but nearly every chain store that sells grocery products also lists prices normalized to some product-relevant unit. These prices are on the shelves, directly next to the actual price, often in another color.

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That is the case in the U.S. as well. Although I've seen unit pricing of products in different sizes use different units (e.g. one product using ounces and the other quarts) that if not done deliberately to make comparison difficult still has that effect.

Not a problem with metric units.

Only if the density is close to that of water. A quick google search says that approximating 1g = 1ml would work for yogurt (1.04g/ml), but not for honey (1.40g/ml).

They don't mark out honey in different base units. Some things are sold by volume, but even yogurt is sold by mass. It's partially because packing density is rather variable between different sources/grades, and also not as easy to handle as weight (just add on top, and don't care about the shape of the contents of the bowl).

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