Firstly, make sure that the layer in ArcMap is visible at all scales, and that it is on/visible. If the layer has a definition query, delete the definition query (this may not strictly necessary, but it is the easiest way to ensure that the definition query is not interfering).
Next, right-click on the layer in the table of contents and choose Edit Features -> Organize Feature Templates. Go through the process to make sure that the layer has feature templates created (ie, use the 'New Template' button at the top). It is these templates that appear in the Create Features window.
Editing Existing Features
As discussed in comments, if you only have a basic license, there are several limitations to your editing, including not being able to edit feature classes that participate in relationship classes. You can safely delete the relationship classes without affecting the data. But the client may need to be aware of this being done so that they can handle the data appropriately when it is returned to them (eg, re-create the relationship classes, or import the data back in to their original database).