For the Received not Invoiced, follow the suggestion above to get to the Received Not Invoiced Report.
For POs that are completed but not moved to history, this happens for two reasons. One is the Received Not Invoiced situation above. The second is, for example, you order 10 pieces, receive 9, invoice match the 9, then calcel the 1. The cancel process will not move the PO to history. There is a process to do this that has no financial impact and I suggest that you do that regularly. Then the only completed POs not in history will be the RNI ones. This process is in Purchasing -> Routines -> Remove Completed Purchase Orders. Make sure that POP Setup Maintain History all the flags are checked.
We have books on POP, report writing from GP, and Information Flow and Posting that helps you track data through the maze of tables. Check out our web site.