I am new to this device and all the apps that I downloaded have a splash screen; I wonder whether splash screen mandatory on windows phone or not
Splash screens are not required for Windows Phone apps (7.5, 8.0 and 8.1), but they are recommended.
Developers use splash screen because it's hard to guarantee the startup performance of apps, especially on low-end devices such as the Lumia 520.
If the app does not have a splash screen, the user sees a "Loading..." message which is not as visually pleasing.
I assume you mean the lockscreen? Yes, this can't be deactivated.