It sounds like you may need to apply the scale of the cord object. If you have tried to scale it up or down without applying the transformation, you would get a result similar to what you have shown above. With the mesh selected in Object mode, hit Ctrl + A, and select “Scale”. That should hopefully fix the stretching and squashing error.
As for the addition of new iterations, I’d suspect that if your Array modifier was set to “Fit to Curve”, anytime you’d extend or move it that the mesh would generate to fit? I’m not quite sure I have an answer to satisfy that aspect, sadly. Perhaps make your initial mesh only one loop around, if you have it more than one, as that would allow the modifier to more frequently update when you move the curve points. If you want to add or remove iterations at your command, rather than to fit the length of your curve I would recommend switching Fit To Curve to any of the other two options, so that you will be able to add or remove the amount of coil to whatever you would prefer.
Lastly, the Recent Operator is Extrude and Move because that would’ve likely been the last operation you had conducted on the object. It sounds like you are using Left Click Select, so I realize the W key is not the hotkey for the subdivide operation. Instead, with the curve selected in edit mode, you should be able to right click and Subdivide should be an option. At this point, the Recent Operator panel should reflect as such. 🙂
I hope those do a better job at getting you to where you want to be!