It is usually desirable to make titles and quotations stand out from your own text. So saying The Sunday Times article The Price of Fish achieves this objective quite well.
But it is not obligatory - it is a matter of choice.
Quotation Marks, it is short work, like a poem, not a book or long story.
No.
You use quotations for short stories, poems, article, and songs I believe. Everything else is underlined.
Quotations for article titles. Italics and underlining are for full books - and the titles of journals.
Yes, you should put a journal article title in quotation marks when citing it in your research paper.
That depends on what format you are writing in. But basically you do it by whatever article you are talking about within the magazine itself. Like this: Smith, John. "Article Title." Magazine Title (Underlined). Date of magazine: page numbers of complete article. Within the text you must only reference the author name, as long as the rest of the information is in a works cited. Is that what you wanted?
If you mean newspaper or magazine articles, and if you are using MLA format (i.e., for an English class), then article titles should be in quotation marks rather than underlined or italicized. APA or Chicago formats may have different requirements; I'm not familiar with them.
An online magazine article is the same as an article in a paper magazine except you can find it online, usually through the magazine's own website or through an article aggregation site. You can find an example through the given link.
Quotations should fit into sentences:contextually.grammatically.
Smithsonian
Yes; the article title should be placed inside quotation marks, while the name of the newspaper or magazine is italicized.
the magazine Living Without