Say you plug your iPhone or iPad into a friend’s computer. If iTunes is installed on this computer (which it will be on every Mac, for instance) it will automatically open and take a full backup snapshot of the device onto the computer.
The backup will be obfuscated but everything will still be totally accessible on that computer.
How do I prevent this from happening from the iOS device side? (As I do not control the computer in this scenario.)
There are two viable options to prevent backing up to any computer.
Turn on iCloud backup and any iTunes will know not to make a duplicate back up and just get on with syncing.
Lock your device with a passcode so that no matter what the computer asks, the device won't enable a sync/backup session until the passcode has been entered.
You can also set a "don't sync" bit on a per iOS device, but that may not be respected by some computers and also won't help if the operator of the computer wants to try to save any information it can access. I'm fairly certain your photo roll is safe if you use the passcode option, but you might want to test that if you have any sensitive photos in the camera roll.
You can't, it's controlled by iTunes. You can ask the owner to turn off the "automatically sync when iPod is connected" setting, or you can watch for the sync starting and swipe to cancel, but those are your only real options.