how to programatically get the SN for a certain instance of a process ? in what table and database does it reside?

Can you tell more about what you want to do with it? 

Processes don't have a serial number, they have an ID.  Only event instances have a serial number.  You can obtain both through the context browser or through code.  In the context browser, the SN is a concatenation of the process ID, an underscore, and the activitydestinationinstance ID.

I don't believe you will find the SerialNumber as a specific column in a table.  Keep in mind it is generally discouraged to query the K2 databases directly as their schemas do occasionally change.  Instead it is recommended you go through one of the K2 APIs (Workflow.Client or Workflow.Management) or the OOTB reporting SmartObjects.

If you describe the functionality you are trying to develop, perhaps we can provide more focused guidance on which of the above suggestions to use.