The Dynamic Content Menu add-on for the 3D View is very useful most of the time. But, on a project I'm working on, I need to find the intersection between a face and an edge and I can't figure out how to do this through the add-on's menu. How am able to find said intersection?
Not sure if this is what you mean, but the TinyCAD extension might be able to do this.
It doesn't have an "intersect face with edge" operator, but as a workaround it can extend an edge to a face, so you might be able to do this by shortening your edge enough that it no longer intersects said face, then extend it.
Snap the 3D cursor at the end of said edge, set pivot to 3D cursor and scale the opposite vertex towards it.
You can then press W Specials > TinyCAD > Extend Edge to Face
Unfortunately, I'm not quite sure what you mean by "find the intersection between a face and an edge". If you could specify further then I might be able to help you. Pictured below is a subdivided cube in face-select edit mode. Pressing the tab key takes will take you into edit mode. As you can see, the edges define the faces. If an edge were to intersect a face, then it would create a new face. Before this cube was subdivided, the top four faces of the cube were a single face.