Is iron (III) oxide-hydroxide the same as iron (III) hydroxide? Firstly, the Wikipedia article on iron(III) oxide-hydroxide says that $\ce{FeO(OH).H2O}$ is sometimes described as iron(III) hydroxide ($\ce{Fe(OH)3}$). If that is so, does iron(III) hydroxide not exist? 

Secondly, the hydrated iron oxides section of the Wikipedia iron(III) oxide page says that on treatment of $\ce{Fe^3+}$ salts with alkali we get $\ce{Fe2O3·H2O}$ (also written as $\ce{Fe(O)OH}$) and not $\ce{Fe(OH)3}$. Is it the same as $\ce{FeO(OH).H2O}$ mentioned in the Iron(III) Oxide-Hydroxide page? If not, how are the two compounds different?

Thirdly, the iron(III) oxide-hydroxide page gives the following reaction:
$$\ce{FeCl3 + 3 NaOH → Fe(OH)3 + 3 NaCl}$$ 
Doesn't this directly contradict what's given in the iron(III) oxide page? And does $\ce{Fe(OH)3}$ here mean $\ce{FeO(OH).H2O}$.

Fourthly, the Wikipedia page on rust says that rust is composed of hydrated iron(III) oxides $\ce{Fe2O3·nH2O}$ and iron(III) oxide-hydroxide ($\ce{FeO(OH)}$, $\ce{Fe(OH)3}$). What are these hydrated iron oxides and how do they differ from hydrated iron(III) oxide-hydroxides $\ce{FeO(OH)·nH2O}$ described in the iron(III) oxide-hydroxide page?

Fifthly, the page on iron(III) oxide-hydroxide identifies $\ce{FeO(OH).H2O}$ as hydrated iron oxide, while the hydrated iron(III) oxide and rust page have me believing that $\ce{Fe2O3·nH2O}$ is hydrated iron(III) oxide. Are they wrong or is $\ce{FeO(OH).H2O}$ also a hydrated iron oxide?

I would also be interested in knowing the structure of these compounds, whether the water is just hydrogen bonded or if it takes part in some complex formation and where I can learn more about such unusual compounds.
Start with my answer here: What is chemical formula of Bauxite? On oxides and hydroxides of aluminium - that's a quick explainer on notation.

Now, to your questions:


  where I can learn more about such unusual compounds


Easy. Here: The Iron Oxides: Structure, Properties, Reactions, Occurrences, and Uses by R. M. Cornell and U. Schwertmann. ISBN: 3-527-30274-3. PDF link



The problem with iron hydroxides is that there are several polymorphs (same composition, different crystal structures), and they are often mixed together in one sample. Add to that that not all iron is fully oxidised, that these compounds are hygroscopic (they adsorb water moisture on their surfaces), and they can contain impurities of whatever was alloyed with the iron (nickel, carbon, chromium, etc etc) forming even more compounds.

A single polymorph rare exists by itself (but when they do, they are spectacular; examples: 1 2 3). Pure iron hydroxide is usually yellow, and pure iron oxide is bright red. Anything in between is going to be brown. When found in nature it's called "limonite", and when formed by rusting of iron, it's called "rust".