2) To prevent failures, take a redundant secondary device (anyways, each co-pilot would/should have one).
3) "Airplane mode" would be perfectly fine, as the device should store all manuals locally anyways, and need a connection only to be updated with newest content.
Personally, I'd say that something like a Kindle would be better than the Surface for this particular task.
Presumably in case of an emergency, the pilot would always be able to call the control tower to confirm whatever details, even if their tablet was dead, so I don't think it would be a major issue.
IF something went wrong, however, like a pilot panics, or his tablet dies (and forgot his charger), he is still able to radio for help.
I believe the bulk of what goes on the tablet is tons and tons of charts. Airport layouts, maps, etc.
When there is more than one pilot, the pilot not flying the plane usually reads the checklist out loud.
I heard that the reason they tell you to turn it off in flight is so that if something goes wrong people panic less. Not sure how true that is though.