Ben,
The only part of yours I'd take exception to is the statement that "A pump uses a fix amount of energy, supplied in electrical form." Energy input to the motor will vary with flow and head.
Here's a "typical" graph of an industrial centrifugal pump. There's a lot more information here than you'll normally get from the Eheim's, Via's, Rio's, Little Giant's, etc. of the world.
Among the additional info is efficiency, required suction pressure, impeller diameter, motor power at the operting point, etc. Note that many industrial pumps allow you to specify the impeller diameter so that you can vary flow at a given head. No, you can't change the diameter dynamically, but you can specify it up front.
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