Hi Daniel Ingram:
Thanks for posting.
As soon as FileMaker Server starts, it is set to automatically open all database files stored in the default and optional database folders, as well as any folders one level below. When you restart your server machine, it also causes FileMaker Server to restart, which resets the status of your database files. Currently there is no setting that will allow FileMaker Server to remember the last status your database was set to. How FileMaker handles hosting databases can be found in the FleMaker Server 11 Help guide, on page 85 under the section "About hosted databases."
Regarding your second question, there is a difference between having a database closed versus having a database paused in FileMaker Server. If you have your database set to closed, connected clients can no longer access the database file. Setting the database to paused will allow users to still read data from the paused file, but they cannot add or modify data within the database. This is also documented in the FileMaker Server 11 Help guide, on page 85 starting under the section "Managing hosted databases." You can find the FileMaker Server 11 Help guide at the following link below.
Thank you TSDuck for the clear response!