Cannot connect to Apple and iTunes Store
Sounds like it may be Restrictions which is in:


  Settings -> General -> Restrictions


if this is off, check if everything is turned ON for cellular:


  Settings -> Cellular -> Use cellular data for


If everything is ON, then it could be a type of profile installed for blocking these apps at:


  Settings -> General -> Profiles


Remove what you don't know, let us know if you fixed it.