Well, it is possible to define custom properties for the whole graph/diagram (see "Edit" -> "Manage Custom Properties"). You could create an empty diagram, define (and set) the desired properties, save the empty diagram, and start new diagrams by loading the previously saved empty diagram first.
It is not possible to fix the drawing area. yEd is designed around the concept of an infinite drawing area. You could use a backgound image to indicate the area where you should place elements, but this is in no way restrictive (and will be ignored by layout algorithms). Additionally, background images are not stored in GraphML, but are an application setting. Thus it is not possible to use backgrounds with your "template" approach.