My apps show updates are required but there are no updates needed.

Try resetting the App Store:

Close the App Store completely from the app switcher window by double clicking the Home button and swiping up the App Store preview pane until it disappears from the screen. Then sign out of the iTunes Store (in Settings).

Then restart the device.

Then sign back into the iTunes Store and try downloading again.

Also check Settings > General > Restrictions > and make sure that the iTunes Store, Installing Apps, Deleting Apps, and In-App Purchases are all under the Allow section.