If you select a face and hit f, nothing should happen. If you select 2 vets and hit f, an edge is created between them, if you select 2 edges and hit f, a face is made. Blender does not care in what scenarios you use these functions so you can make all kinds of useless geometry with them, or you could make geometry that is useful to you - that is up to you as you are the creator and Blender is a tool.
Connecting verts and edges is one of the most basic functions in modelling in Blender so it would be hard to give examples of the use cases for it as it can be used for pretty much anything. You could do 3d modelling by only duplicating vertices and connecting them to make edges and then connecting them to make faces if you wanted.