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I don't know how to model a "true" spring in Revit (and most would argue that would be over-detailing anyway), but look at >This Thread< for a means of creating one. The example does not include the parametric controls you've noted, but it shouldn't be impossible to control the size of the Profile and then the radius of the Sketch Lines with some cleverly applied constraints. There's also a link in that thread from which you should be able to steal a spring.
Corey D. 
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