Hi Doubled58-
Aperture allows you to store your photos in two different ways: Importing the photos into the Aperture Library itself (Aperture calls these "managed photos"), or storing them anywhere on one or more disks and telling Aperture to work with them and leave them in their current location (these are "referenced photos"). It comes down to personal preference-- if you want everything in one simple library file go with the managed route; if instead you prefer to organize things yourself use referenced images. The drawback to managed files is they are more difficult to get to in the Finder since they are buried in the library file; for this reason when you need to export managed images it's best to use the File > Export command within Aperture, or to use the Media Browser in Mail, etc.
To rename one or more photos simultaneously, first select them in the Browser (or Split View, etc), then select Metadata > Batch Change.
Select an appropriate format from the Version Name Format popup and enter a Custom Name if desired. This will rename all of the selected photos within Aperture. If you want to rename the image files on disk as well, check the Apply to Original Files box.
As for your last question: Aperture allows you to have as many photo libraries as you'd like, and you can switch between them at will. If you no longer need the "Aperture 3 Trial Library" or any of the photos within it you can simply drag it to the Trash. The next time you start Aperture it will present a dialog to create or choose a new library. You can also create a new library within Aperture by selecting File > Switch to Library > Other / New, then click the Create New... button. After you choose a name and location for the new library, Aperture will switch to the newly created empty library. You can then move the Aperture 3 Trial Library to the Trash.