Exposed metal rod in the wall. What is it? What should I do?
Before electricity, gas lighting was common in homes and commercial buildings.  When electric lighting began replacing gas lighting, sometimes gas piping was disconnected from gas and used for electric lighting.  There are even some reports that for a time, gas piping was installed new for electric lighting - the idea was that just in case electricity turned out to be a novelty or fad, the piping would be in place for gas lights.  

The picture is not very clear but it appears to be a very corroded pipe with a gray flat cable in it.  

The bend in the pipe is sharp, unlike electrical conduit, which is usually bent with a gentle sweep.  Judging from the brickwork, the plaster, the stair stringer, and the advanced deterioration of the pipe, it could be 100+ years old.  

I believe it is most likely old gas / plumbing pipe being used for electrical.  The gray flat cable in the pipe might be UF - nonmetallic cable rated for wet locations - that's typically the only flat gray cable you see in recent years.  However the current conventions for color coding the jackets of nonmetallic cables have not been around nearly as long as this structure, so it may be something else.