Hi, do you by any chance use the "Power Save" feature (Avast Mobile Security, see the Menu)? It can enable the Wi-Fi.
Regarding the App Lock, there are two options:
1) It is either being disabled by a power saving functionality of your device; when the app is not running, it cannot apply the lock-screen
2) Or you have set the "App Locking timeout" for some value higher then 0 minutes. It means that when you unlock an app, all other apps are also unlock for the period of the timeout set. If you want the lock-screen to be always on, go to Menu → Settings → App Locking → App Locking timeout and set it to 0.