Introductory: Have you tried going into Settings >> Mobile Data and de-selecting Mobile Data? Normally, when you install apps from Google Play, the App Permissions will tell you what apps have network access. Having said that, it could be any number of applications turning on your Data.
Second Possible Solution: You may also want to try disabling automatic connection by pursuing the following action. go to Settings >> More Connections > Mobile Networks > Network Mode. Make sure that none of the modes have automatic connection enabled.
Answering Your Questions: As far as I'm concerned, you can download Permissions Explorer to see what apps are capable of accessing your Data.
Good luck and let me know if you have any other questions.