How often do authors send their paper by email upon request?
Cambridge did a limited survey on this, based solely on requests that came via the repository (so not by direct email). They found that:


38% had the author send the paper directly via the repository
4% of requests were explicitly denied by the author


This leaves 56% unknown. A later followup survey of authors who didn't use the repository response function suggested that about a third went on to contact the requestor directly, suggesting an overall success rate comfortably over 50%.

(As an aside: the repository I manage involves us forwarding such requests to researchers, and we have no "click to send a copy" function, so I get cc'ed on a large number of the replies. Counting only the cases where the author is still around, I would estimate that over two-thirds get a copy of the paper, and it's quite common to see replies that amount to "hi, here's the paper, here's also a few others that look relevant to what you're interested in". I don't have solid figures on that, but given that my academics are fairly similar to theirs, it leads me to suspect Cambridge's success rate may be higher than they expect.)

Interestingly, the Cambridge repository data suggests that about half of requests are for material that is simply not available yet - it's listed on the repository on acceptance, but not yet published online by the journal - and so there is the complicating factor that some authors were reluctant to share the paper "before publication". This would of course not be an issue for people contacting the authors of a published article, which by definition is already out there.

There was no data on academic/non-academic email addresses in the Cambridge survey, but purely from anecdotal observations in my own repository, I would say a) academics will often write a more engaging request ("I am doing some work on X and would like to see the data on Y which I think is relevant", rather than just saying "research" or giving no reason at all), which is probably more likely to encourage a response; and b) in a lot of cases, people will state an academic affiliation but use a private (or not-obviously-academic) email address. This is true for both researchers and students.

[edit: I checked today. Of the last twenty requests, 12 used an academic email address, 7 were apparently from academics (or students/researchers) with a non-institutional email address; only one was clearly from a non-academic]

This is all repository-based data. Direct emails to authors may have different response rates, but I suspect this is the most effective wide-scale monitoring approach we have without a (rather invasive) experimental campaign...