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You need an MDM to manage it remotely. Something like Jamf Now is $2/device/month. Not sure how much the shipping costs, but might be break-even

Splashtop will let you view an ipad's screen. It's fiddly to start (remote user has to allow access, enable broadcasting, etc every time, and this is a non-trivial step to get over), but it does work, in the sense that seeing the screen is faster than just guessing what is going on as your panicked user pokes randomly at things no matter what you say, leaving you with no context.

It is functional enough to be useful, if the other person on the line is good at following instructions.

Sure you can. Look into MDM services like Jamf Now.