If the question is auditing for unauthorised access then you have to identify the tables and previledges and set up auditing accordingly. This is resorce intensive and should be done only if needed.
As far as checking the database health check for the following;
1. Enough free space in tablespace & Sufficient contiguous space in the tablespace to accomodate growth of large extents.
2. List of segments approching max extent limit
3. Monitor Fragmentation of table & index and do reorgs/rebuild index
4. Monotor SGA for databuffer quality, SQL pin & hit ratios, buffer waits.
5. Monitor rollback segments for header waits.
6. Monitor system events for excessive waits.
7. Monitor memory & disk sorts
8. Monitor redo log buffer for excessive space requests.
9. Identify I/O bottlenecks and do IO load balancing.
Buy this book and you have lots of scripts that a dba needs in day to day life. I don't say all the scripts will work, but if it doesn't work, you will make it work and customize it the way you want, as its part of your work by profession.
If you could ask specifically the kinda script with the kinda details, probably I will provide if I have one in script library.
you can reach me firstname.lastname@example.org