System so slow; permanent WiFi activity
OS Monitor might prove helpful here. Amongst others, it shows you all current connections including their stati, always along with the target IP (which you can even get WhoIs details on, see screenshots) and the app holding it. This might at least help you to narrow down possible candidates.

 
OS Monitor: Open connection, connection target details (source: Google Play; click images for larger variants)

Hint: To transfer data, the connection status must be ESTABLISHED.