How can I tell a GPS installation is acceptable for IFR use?
The easiest way is to read the Aircraft Flight Manual (AFM) or Aircraft Flight Manual Supplement (AFMS). If the the GPS was installed at the factory, it will be addressed in the AFM. If it was installed later via an Supplemental Type Certificate (STC), there must be an AFMS to cover the operation of the GPS.  

If the GPS installation was not at the factory, there should be an a/c logbook entry showing the installation and STC approval.  

As specified in AC 20-138D:  


  19-9. Operations manual or AFMS/RFMS.
  
  An AFMS/RFMS must be provided that contains the limitations and
  operating procedures applicable to the installed equipment
  configuration. The AFMS/RFMS must address the operation of the
  equipment and the related components as they are installed (e.g.,
  remote source selector). An AFM/RFM supplement is required if the
  installation is based on a prior approval that had an AFM/RFM, or if
  there are any limitations associated with the operation of the
  equipment.


The key information is covered by the first sentence -- limitations and operating procedures. If the GPS is not approved for IFR, there must be an operation limitation in the AFM/AFMS that states that (and in all of these cases I've seen, the FAA also required a placard stating "GPS not approved for IFR flight.")  

If the information is not included in the AFM or AFMS, I would question the approval of the installation as all installations require the AFM/AFMS.  

As for the database, it expires every 28 days. Turn the GPS on. If the database is not present or expired, you will get a message to that effect.