Should running number be separated column from primary key in database?
Your Primary Key is a unique key and should be sufficient to find the records that you need.  However, if you need a sequential number for other identifying reasons, then YES you should make it a separate unique value.

I personally would skip the GUID key and just use the Integer, but that is a choice you will need to make.  

Getting a sequential set of keys without gaps will require some code.  Are you using Microsoft SQL Server or some other version.  If MS SQL Server, look at:

http://msdn.microsoft.com/en-us/library/ff878058.aspx 

This is a discussion of using Sequence Numbers, with some warnings about the limitations.