Random faces appeared on object I'll start with pictures:



These are not vertices... they are faces, but I don't know how they got "duplicated" or what. As you can see down, in the 3D Viewport's footer, I'm in face selection mode.



How do i fix this without deleting that edge or face? Because if I delete it, I'll have to redo it all again...
You have probably started an Extrusion (E) and then "accepted" it without moving the vertices, effectively creating a zero-width rim.

Problems like this are easily fixed by selecting all your vertices and doing W > "Remove Doubles" ("remove double vertices" since Blender 2.8)