The exposed wires look ANCIENT - I'd recommend new fixtures (from context, it sounds like you bought the place).
The shade in the second picture needs to be replaced - it's not safe. It looks like it was intended for a table or floor lamp, cut away to fit the sconce. That's not the dangerous part - it's designed to clip onto the globe of a type "A" (standard) light bulb, but you're using it with a CFL. The coils are NOT meant to be put under any sort of mechanical stress.
We're renting, but our landlord is letting us fix up the place for discounts on rent money. It works out, but the trailer is quote old and can't be replaced. If we were to move in a new trailer, we'd have to find a new place to live because PA has a law that every house or whatever has to be situated on at least 2 acres of land.
That second picture is actually a table shade, yes, which is why I said I don't know what I'm doing. I realize it's a hazard. I don't put the lampshade on if I can help it (it is resting the coil on top of the CFL bulb, though). I'm ashamed to say that I had no regular light bulbs in the house but I did switch it out right away. Those things are nice but not very bright for the way the hallway is set up.
I talked to husband and he said that we would get new fixtures, but for now we are blocking them off from tiny fingers (they are roughly 6 feet off the floor) and taping the exposed bits and socket with Gorilla tape to keep them from being exposed.
My poor home is all tore up.