1) a wire with a rectangular cross-section coiled into a spring, or a round wire coiled/bent along a rectangular path? Either way, probably best to use a 3d-sketch to draw a path and then sweep the wire cross-section along this path.
2) assuming the spring is bent/curved in 1 plane only, it's do-able. In the past I've used a 2d sketch to draw a curved zig-zag which I can only describe as an accordion, starting on the vertical (or hoizontal) you know the angle and radus of the end of the curve, so draw that. Knowing you want say 5 coils you can then divide this total curve into 10 (no of coils x 2) and these intervals, along with the spring diameter, will give you locations along the curve for the peaks & troughs of the spring. Use these to give you points in the 3d sketch to then draw lines and rads to give the spring's path. Create a new plane at one end of the spring and draw the wire's cross-section and sweep it. Just take care with the cross-section's size compared with any rads along the path, if the cross section is larger than the rads then the sweep will fail.
3) using about - have the start angles constrained but the end angle adaptive. All internal angles a parameter of the total divided by the coils and see how it goes. I can imagine the sweep will fail as soon as the coil gets compressed tightly but should work ok for a good range of angles.
Considering this basically involved sketching the profile of each loop and then plotting the path for each loop in the 3d-sketch I think you'll soon go mad if it's any more than a few coils, so assess the need for it before starting
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In addition to the information sam_m provided, attached is an example file created and saved in Inventor 2010 (that's as far as I can go back currently). This file contains a Height and Bend parameter that are animated using the Studio environment, using the Animate Parameter tool.
You might see this link also, as JDMather has provided a more refined example of a rectangular spring technique: