I have a more general response rather than answers to the individual questions. (Though I suppose this is largely an answer to the sixth question.) I think the question “how has the internet changed the way we write?” is slightly misdirected. I think that genre informs writing to a much greater extent than the technological substrate or the means of distribution. The way I write a review or an interview is determined by the conventions of the genre. If the internet is a factor, then it’s in WHAT I write about rather than how—the internet provides more space for coverage of emerging artists, or to put it another way, editors of online resources are generally more open to covering their work than print editors.
In other words, the way I write for Twitter or Yelp is just as different from how I would write for Rhizome or another online art publication as it is from how I’d write for print editions of Art in America or Artforum, because the tweet and the yelp review are generically distinct from the art review, the art essay, and other genres that the internet has inherited from print media.
Of course, the internet has allowed particular genres to flourish and develop. It would be interesting to track the appearance and growth of terms like “thinkpiece” and “longform” and think about them as internet-specific formats (here’s a casual, unresearched observation: I think beginning an analytical essay with an autobiographical anecdote is one common feature of online longform writing). Genres like blog posts and listicles (that have become common in art writing thanks to Art fag city, Artnet, Hyperallergic, and the like) are geared toward the “measurable attention” and social-media circulation that you bring up in your questions, but again I think it would be more productive to think of these as genre-specific features rather than media-specific ones, because most online writing in older, print-informed genres is done without much consideration for hits and views.
Your question about attention strikes me as problematic because your definition of attention seems to be grounded in the kind of attention cultivated by print culture, rather than allowing for the sort of ambient attention that is common now, and affects the way people read print media as well as online media.