App to turn iPhone to an old style feature phone?
There will not be an app for this as apps are not allowed to change the system in this way.

The closest you can get to this is iOS Restrictions, which require a passcode to re-enable access to certain features on the device. You can configure which features are restricted on the device in Settings → General → Restrictions. There is no automated schedule for Restrictions — you will be required to enable it and disable it yourself.