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We are talking about turbines for extraction of energy from a fluid.

Consider a typical wind turbine, or a francis turbin for water - we have one hub with on set of vanes that are driven by the medium.

Now, consider a typical turbine in a steam engine - here we have alternating moving vanes and fixed counter-vanes. The fixed vanes redirect the flow after each stage, something that's apparently not neccessary in a water turbine for a high efficiency.

1 - My intuition tells me that this has something to to with the change of temperature or entropy along the turbine. Is this intuition correst?

2 - Why are the turbines built differently? Assuming it's not possible to extract a reasonable amount of energy with a one-stage turbine from steam, why is that so?

3 - Assuming an appreciable pressure drop without a big change of temperature along the turbine (maybe a pneumatically driven turbine), will I still need a multi vane design to extract most of the energy?

Bonus question - can the same reasoning be applied to pumps or compressors - a multi stage design is neccessary for decent efficiency if a significant temperature change is involved?

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In a gas turbine (I'd expect a steam turbine to behave similarly), the efficiency with which rotors (moving vanes) extract energy from flow is dependent on the angle between the blades and the relative flow velocity; the optimum value of that angle is influenced by compressibility effects at high speeds. The stators (fixed vanes) turn and re-accelerate the flow (the gap between blades is a nozzle), maintaining an appropriate angle of attack for the subsequent rotor blades. If a rotor stage increases in radius too far, Mach effects appear near the tips (big efficiency loss); the aerodynamic efficiency of the airfoils in the blades peaks at a given stage pressure ratio, such that a desired turbine pressure ratio is most efficient when assembled from multiple stages.

The flow velocities experienced by a wind or water turbine are so much lower than those in a gas/steam turbine that Mach effects at extreme tip radii do not occur; absent a radial constraint, the single stage can be expanded until the total energy extraction desired is achieved, and the airfoils shaped for maximum efficiency at each radial location.

As far as fans/compressors/pumps, compare the propellers on late-WWII fighters to the multi-stage compressors on early jets. When the freestream flow velocity is low, it's more efficient to extend in radius; when it's high, it's more efficient to extend in stages.

Ultimately, energy addition/extraction is a function of $\dot{m} \Delta V$; gas/steam compressors/turbines have a high $\Delta V$ to work with, but are restricted in $\dot{m}$, whereas wind/water pumps/turbines have a low potential $\Delta V$, so have to increase $\dot{m}$.

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