How do I subdivide all faces in a mesh equally? I want to subdivide all faces at the same time (subdivide in edit mode doesn't subdivide them equally) the way it can be achieved in sculpt mode with SculptDraw brush selected, strength set to 0 and detail set to a low number (1px) and then sculpting all over the object. Is there another way (I'm using v2.79 and the only reason I want to do so is to be able to use the Displace Modifier)?
Welcome to Blender Stack Exchange!

I know of a couple of options that will do what you're looking for.

The first is using sculpting like you're doing already. However, in the dynamic topology settings, there is a button called Detail Flood Fill. This applies the selected detail level to the whole object without having to manually sculpt.

Blender also has a modifier called Remesh. Add this modifier (second column about halfway down in the list of modifiers), set the mode to Smooth, and turn up the Octree Depth a bit.