Rusting: alternatives to water?
Rust is by definition the transformation of iron metal to iron oxide (and iron hydroxide as an intermediate). You cannot "rust" other metals, although you can form oxides and degrade them etc. It's just not called rust when you convert, e.g. $\ce{Cr}$ to $\ce{CrO3}$. So there is only one rusting process.

1) Water is not a catalyst in the reaction that forms rust. A catalyst by definition is not consumed during a reaction (its bonds are not broken). Water can be and is the medium that carries $\ce{O2}$ to the iron (otherwise $\ce{O2}$ from air can react with the metal), and it is consumed in the process by dissociation. The fact that it is reproduced does not make it a catalyst. First iron atoms are oxidized by $\ce{O2}$ as in:

(a) $$\ce{Fe + O2_{(aq)} \rightarrow Fe^{+2}_{(aq)} + 2e-}$$

Then the free electrons are quickly absorbed by free protons from water by:

(b) $$\ce{2e- + 2H+_{(aq)} \rightarrow H2}$$

It is highly unlikely for $\ce{H2}$ to react with $\ce{O2}$ to form water -- that is a combustion reaction, so high heat or pressure would have to be added. Rather, water is reproduced by a different reaction (d), below.

2) "Dry" rusting is not possible because the process requires reactions with water's ionization products $\ce{H+}_{(aq)}$ and $\ce{OH-}_{(aq)}$ (notice the aqueous states of all ions). The process continues by production of iron hydroxides:

(c) $$\ce{Fe^{+2}_{(aq)} + 2OH-_{(aq)} &lt;=&gt; Fe(OH)2_{(s)}} $$
(d) $$\ce{Fe^{+2}_{(aq)} + 4H+_{(aq)} + O_2_{(aq)} &lt;=&gt; 4Fe^{+3}_{(aq)} + 2H2O_{(l)} } $$ 
$$\ce{Fe^{+3}_{(aq)} + 3OH- &lt;=&gt; Fe(OH)3_{(s)}} $$

This is why more acidic media produces rust faster; it pushes (c) and (d) to the right because (b) consumes free electrons and renders more $\ce{Fe^{+2}}$ for further reaction.

Finally the iron oxides "dry" to form the actual rust compound, which is a hydrated oxide: $\ce{Fe2O3\cdot nH2O }$.

3) You can see by now that water is the required solvent because the reactions of interest all involve $\ce{H+}$ and $\ce{OH-}$.

One could say there exists a "rust triangle" where "time, oxygen, and water" are required as an analog to the "fire triangle": heat, oxygen, and fuel.