How I can monitor SQL Server 2012 databases to determine the security privileges that are called by different processes
You can use SQL Activity Monitor. This will show the current queries executing in your SQL Server instance with below details


SPID
Login
Database Name
Task State
Command
Application
Wait time
Host Name and many more under PROCESSES tab


Also you can have a look on


Resource waits
Data File I/O 
Recent Expensive Queries