The OED defines opacity as "the quality or fact of being opaque; opaqueness." Opaqueness is "the quality of being opaque; opacity." I'd take this to mean that they are synonymous. The former was borrowed from French, which of course came from Latin. The second takes the root straight from Latin and applies an English suffix to it instead. And they were both coined or borrowed at roughly the same time, so they've coexisted now for roughly 400 years.
Sometimes when there are pairs like this, there are different shades of meaning. Or sometimes people think that there are different shades of meaning, but oftentimes usage history doesn't back it up. If there's any difference in meaning, it's that opacity has more extended and metaphorical senses, but that's most likely because opaqueness has never really been used much. Google turns up only 149,000 hits for it to almost 2.5 million for opacity.
And finally, both opaqueness and opacity are indeed nouns, and opaque is an adjective. I don't know what your son means by "opacity means that the item IS opaque." And as to how I use them, well, I don't use opaqueness. It sounds clunky to me, but that's probably because I virtually never hear it.