An interesting, and useful, but largely overinflated concept. Unfortunately, data decays faster than the average historian is capable of appreciating.
Diaries/autobiographies are only primary sources insofar as they describe what happened to (or extremely near) the author. They are secondary sources for anything else peripheral to that.
Newspaper articles are practically never, ever, ever primary sources with regard to their content. Usually they are just interview notes assembled into an entertaining narrative. Even on the off-chance that the article writer is talking about something that actually happened in their presence, they are compelled by the pressures of the occupation to spin it into something that it largely is not. Not only is news made up of fabrications to a greater or lesser extent, but it is also predicated on anomaly -- what is by definition not the usual state of affairs. Man bites dog. Such a medium is inherently unsuited for the discovery of what the usual state of affairs was in the past.
The idea of a law as a primary source seems meaningless to me. It's not a source at all. It's the thing itself. It's the logical equivalent of being there, isn't it? If you have the original event, you don't need a source. But this then delves into metaphysical concepts such as "what is the law, the idea or the written words?" and it does not really bear examination here.
A portrait may be a primary source, at least if the subject actually posed for it, but that being said it is also just about the least reliable type of source for anything. Portraits hardly bear consideration as a source of information at all, for all the good they do. They only are included, in my opinion, due to a deep-seated desire for humans to associate names with faces, regardless of how spurious the face might be. How many different faces does Columbus have today? What about Jefferson?
So now we can be clear about something. "Primary sourceness" is not an attribute of the source, but depends on what is being sought from it. A diary might be a primary source for what has happened to its author, but it is a secondary source (at best) for a story told to the author by someone else and committed to the diary. And how much of one's reality qualifies as a story told to one by someone else? Quite a lot, if you think about it. It is possible, and unfortunately all-too-frequent, for a canonical "primary source" to be milked for details that it can't possibly support with any real amount of reliability.
Primary sources are also not infallible or necessarily authoritative at all. Human psychology is such that two people will rarely agree on every detail of a complex event which both witnessed. In fact, they tend to settle the details in their own minds long after the event is over. Nor is there any deterministic algorithm for divining the truth between them, and in principle there cannot be. The person assigning the weights and methods of such an algorithm is introducing arbitrary criteria into the question.
All we actually know of history from historical accounts such as those listed above are whispers, rumors, half-truths, lies, mistakes, propaganda, and distortions. History is not accurately reflected in what has been written or depicted during, or about, the past. Even photographs distort by erasing all context outside the camera's frame. What can we get from these, at best? A vague idea, sure. A definite understanding? Not without archaeological evidence to corroborate it. Archaeology is how we know Herodotus was massively full of shit and Thucydides wasn't. It's how we know Troy was a real place and Atlantis was not. It's how we know that there were probably never large numbers of Hebrew slaves in Egypt, and that Exodus is almost certainly a work of fiction written during the Ptolemaic Dynasty, with the Moses myths being based largely on the real and legendary exploits of Alexander.
Modern historians overrely in narratives (like Suetonius) and underrely on relic-evidence (like the ruins of the Circus Maximus). This is an artifact of history departments being associated with literature departments in colleges, and the two fields being taken up as subjects by the same sort of people. Younger historians sometimes even believe that history is basically a form of literary analysis or deconstruction. A history of maps is not a history of territories, Sonny-Jim. Knowing what people thought or believed or valued in the past is not tantamount to knowing what happened in the past.
And in regards to Herodotus being massively full of shit, it's ultimately him you have to thank for this dubious tradition of history-as-narrative.