Hi Mark
Dan's reply is useful and detailed. I'll just reply to your first query in the second paragraph. You can install Moodle on localhost with XAMPP, then export the course as a .mbz backup and import that to the local installation. That's not so difficult for a tech, and indeed you may already know about it, in which case my apologies for telling granny how to suck eggs. That would allow the student to do their course offline, though how well a local installation would obey selective releases I'm not sure. You'd need to do a trial run.
I'm a Moodle development newbie so can't answer your second query, but for sure I'd be very interested in any answers posted here or elsewhere. I strongly suspect that a plugin would be needed to detect an Internet connection and then send data, as I very much doubt that this is part of Moodle core. Again, though, I write from relative ignorance, and welcome and actively seek enlightenment from gurus
Fred