There is no OS installation that a user can perform. At the same time, all updates for OS and apps (mobile applications) are pushed by Apple, but authorized by the user. Note that iOS 6 on iPhone and iPod is fairly buggy. The update drains the unit's battery in a matter of an hour or so. If you are running iOS 5, there is nothing more you can do as there is no iOS 7 update for iPhone and iPod. This does not seem to be a problem in iPad, which seems to run iOS 7 smoothly.
At the same time, all apps are installed from Apple's App Store. This means that no vendor can distribute any software without Apple checking it first for malware and/or performance a fairly costly process, about $800 for a developer's license (last time I checked).
Aside from downloading files from the internet or from a service like Dropbox to an iPod, iPhone or iPad, there is no access to the device storage other than using the iTunes program for Mac and/or Windows. With iTunes, you can merely transfer multimedia to and from the device.