Media, like data, is the plural form of a word borrowed directly from Latin. The singular form is medium. In the 1920's media began to appear as a singular collective (mass) noun. This singular use is now common in the fields of mass communication and advertising, e.g., The media is (or are) not against businesses. When media refers to the mass media, it is sometimes treated as a singular form, e.g., "The media has shown great interest in these events." Many people think this use is incorrect and that media should always be treated as a plural form, e.g., "The media have shown great interest in these events." I would say: The mass media IS...

Since the word "media" comes from the Latin plural of "medium", the traditional view is that it should be treated as a plural noun in English. In practice, in the sense of ‘television, radio, and the press all together’, it behaves as a collective noun (like "staff" or "committee", for example), ad those are treated as singular. Which means that it is acceptable in standard English for "mass media" to be treated either as singular or plural. So, pick what you like better. Unless you're writing for a publication, then consult their style manual. FWIW, I personally still use it in the plural. Too much Latin background. ;)

Hmm that's tricky. Well "mass media" refers to a very large network that consists of many different components of the "media," combined into one. Though "media" is the plural of media, "mass media" refers to that one large entity, so I would say singular. Therefore, "The mass media IS spreading this story."

Since media is plural, then you should use "are". "Mass" is just an adjective that describes "media"

And here's my summary of the usage note: a) It depends, and b) experts don't agree. If you can give an example of how you actually want to use the phrase, then perhaps we can figure out which of these parts of that usage note apply! Personally, I would handle this by rewording the sentence to avoid the problem. For example, instead of saying "The mass media are becoming less and less professional," I could say "All modern forms of mass media are becoming less and less professional." Do you see what I've done? The subject is no longer "media," it is "forms," which is unequivocally plural.