The standard location for app files is ~/Music/iTunes/iTunes Media/Mobile Applications.
There are no redundant duplicates in a device's backup, on either iCloud or locally via iTunes.
Situations like this illustrate why it's a good idea to back up apps to iTunes' library, and to have secondary back ups of the essential apps in that folder.
Apple has made that more difficult by disabling most of the app transfers between devices and iTunes 12 (due to App Slicing) and forcing users to rely on automatic downloads from the cloud to keep up to date, but they are of no help if an app is pulled from the Store, or a new version turns out to be less desirable.
Some users boast of never having connected their devices to iTunes, but there are many good reasons to do so.