ArcMap- catalog- can't delete a feature class

TimAnderson5

I am using ArcGIS for Desktop 10.4.1. I have a gdb on a folder located on a network attached storage device (NAS). If I right click on a feature class to delete it, "delete "and "rename" are grayed out. New feature classes can be created in the gdb but cannot be deleted (or renamed), including feature classes that have no features within them. This also goes for anything in the gdb including rasters, although rasters can be renamed but not deleted.

I don't experience this with gdb's on my computer hard drive. Is this problem happening because the gdb is on a network folder?  If so, how can one work with gdb's on network folders? Below is a screenshot of the catalog view.

TimAnderson5

I believe I figured out the reason for delete and rename (for feature classes) being grayed out, which was that I had an editing session open and had forgotten to stop the editing session.

However, now I am finding that I cannot add feature classes or rasters to the geodatabase using Spatial Analyst tools (Extract by mask or Contours). I can add rasters or shape files to the folder located on the network drive but not to the gdb within that folder; I do get error messages related to permissions. It appears to be an issue limited to Spatial Analyst tools creating features or rasters onto the gdb located on a network folder. If I use Spatial Analyst Contour tools to create contours from a raster DEM with the destination into the gdb in the network folder, there are no error messages but it creates an empty polygon feature class with a table type symbol in the gdb; but I can create a contour feature class with the Spatial Analyst tools onto a gdb on my computer hard drive. 

I created the geodatabase on the network folder by simply right clicking on the folder to create a new gdb. I am not using an enterprise version so I don't have a Version Manager view. I can use the Spatial Analyst tools to create feature classes within gdb's on folders that are on my computer hard drive; but I cannot copy those feature classes onto the gdb located on the network folder. I read something about the need to load MS SQL Express but that is getting more complicated than I had hoped it would need to be. I didn't realize that working from an NAS should cause such complications. I am not sure of a work around to work on the hard drive but save it onto the network drive, which gets backed up for crash security reasons.