Why are both the zero and definite articles used with these phrases?

The zero-marking used by newspapers in such contexts as yours or in any formal written texts does not fit any entry in the rules given by ordinary grammars. In Wikipedia I found this entry that is not really related to your contexts, but might give us a hint to why the "zero-article" was used in some of your sentences:

The zero article is also used in instructions and manuals. In such cases, the references in the text are all definite, and thus no distinction between definite and indefinite has to be made.

I would concentrate on the sentence no distinction between definite and indefinite has to be made. It is true, sometimes the issue discussed by a newspaper article is so widely known, that no distinction between definite and indefinite is necessary.

However, it is clear from your sentences, that the omission of the article has not occurred because of that necessarily. I believe this is more a matter of style in writing: newspapers are known to drop articles especially in their headlines for more impact.

See for example

Cabinet backs PM over no-deal Brexit and Iceberg threat to seals and penguins from the BBC news

or

Facebook's advertising integrity chief leaves company and Romney urges sweeping vaccine plan... from Reuters.US

I will not quote such occurrences in the body of the articles, since you have provided plenty yourself. While researching for this answer, I came across another EL&U answer that coincides with my intuition. Omission of the article definitely make the sentences sound more formal, almost axiomatic, if I may say so.

If you look at (B), (C) and (E), you will see that they do sound more like headlines, as if claiming more authority for the information they provide. Where the article is used, the sentence is intended to be more neutral so that the reader's attention be not distracted by that particular piece of information, but look at the global meaning that transpires from a whole paragraph let's say.