Networkmonitor

Most apps transmit data when you don't see it (e.g eMail apps, messaging apps..). This app is able to protocol which apps transfer data and logs it. Additionally it is saved whether the data was transferred over WIFI or a mobile network (your cell provider). This allows you to view detailed information on when your data limit was exceeded and so on.
This information can be presented in a always-on-top window (called overlay) which shows you the current upload/download rates and the apps which are currently transmitting data.
Bear in mind that the app periodically pulls data from your phone (every second at the fastest setting) which, even though the algorithms are optimized, could drain your battery faster. The best approach would be to disable the overlay and only enable the logging, as it fastens the whole process a bit.

Users of Android 6 have to grant the app to draw this overlay, when it hasn't been done yet.
Please report all kind of errors you encounter or suggestions you come up with to me at [email protected] or down below in the ratings.