Obtain precipitated iron?
Is it possible to obtain pure, precipitated iron with no oxidation by some chemical process?


Very pure iron can be obtained by pyrolysis of iron pentacarbonyl.  Iron metal obtained in this manner is in fact called carbonyl iron and is commercially available.

$$\ce{Fe(CO)5 -&gt; Fe(s) + 5 CO}$$

Doing this yourself is very dangerous, however, because iron pentacarbonyl is volatile and toxic.  The decomposition reaction to produce iron requires high temperatures, and the byproduct is carbon monoxide gas, which is also notoriously toxic.


  Alternatively is it possible to electrically purify iron using an anode and cathode?


This is also possible.  I don't know about other salts of iron, but to form iron from iron oxides, very high temperatures are required.  The other answer mentioned Dr. Sadoway's work.  Let me highlight a recent article of his unveiling new anode materials for electrolytic decomposition of iron oxide.  At temperatures as "low" as 1538&deg;C, molten iron oxide can by electrolyzed to pure oxygen gas and to molten iron metal using electrochemistry.

Water is not an appropriate solvent for electrochemical formation of iron metal.  At potentials low enough to favor $\ce{Fe^0}$ formation from $\ce{Fe^{+2}}$, water is unstable and would be reduced to hydrogen gas.