How can I see how much internet bandwidth each process is using at the moment?
Simple System Monitor does that

Relevant feature from app description


  View list of active apps and processes and their CPU usage, RAM usage, network activity, PID and UID. 


If you monitor the Active Processes tab you can see the change in data usage. You can order the view based on parameters as shown in the second screen shot. The default update interval in settings is 3 seconds which can be varied as per need. If you worried about battery consumption , you can pause the app from the menu option on top left