Why are there no organisms with metal body parts, like weapons, bones, and armour? (Or are there?)
There are some cases, as hinted at by the comments. But these are relatively small amount of metal.  

Its not that there is no metal available, but I can think of several reasons you don't see iron exoskeletons on animals all the time.  Firstly, fully reduced (oxidation state 0) metal has a high energetic cost to create in reduced form.  

Iron is the second most common metal after aluminum on the earth's crust but its almost entirely present in oxidized states - that's to say: as rust.  Most biological iron functions in the +2/+3 oxidation state, which is rust or closer to it than metal.  Cytochromes and haemoglobin are examples of how iron is more valuable as a chemically active biological agent than a structural agent, using oxidized iron ions as they do. Aluminium, the most common metal on earth has relatively little biological activity one might assume because its redox costs are even higher than iron.  

If there are some reasons why reduced biometal doesn't show up very often, inability of biological systems to deposit reduced (metallic) metals is not one of them.  Bone and shell are examples of biomineralization where the proteins depositing the calcium carbonate or other oxides in the material are structured by the proteins to be stronger than they would be as a simple crystal.  There are cases of admittedly small pieces of reduced metal being produced by biological systems. The Magnetosomes in magnetotactic bacteria are mentioned, but there are also cases of reduced gold being accumulated by microorganisms.  

I would say that while iron skeletons might seem to be an advantage, they are electrochemically unstable - oxygen and water will tend to oxidize (rust) them quickly and the organism would have to spend a lot of energy keeping it in working form.  Electrical conductivity sounds useful, but the nervous system favors exquisite levels of control over bulk current flow, even in cases like electric eels, whose current is produced by gradients from acetylcholine.  

What's more, it is a fact that biological materials actually perform as well as or better than metal when they need to.  Spider silk has a greater tensile strength than steel (along the direction of the thread). Mollusc shells are models for tank armor - they are remarkably resistant to puncture and breakage.  The time it would take for metalized structures to evolve biologically might be too long - by the time the metalized version of an organ or skeleton got started, the bones, shells and fibers we know probably have a big lead and selective advantage.