Parabola questions galore!

I'm a newbie with a pretty specific set of questions to ask.  Questions that I have acquired over an arduous past couple days.  Questions that make me a nightmare for experts like you.  Answer my questions and that will be the end of it.  I will not look for you, I will not pursue you. But if you don't, I will look for you, I will find you, and I will continue to ask the aforementioned set of questions.  Good luck.

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Question 1:  How do I go about measuring the arc length of a parabola in Rhino? In a nutshell, I'm looking to accurately measure curve length in Rhino in this case using a parabola.

Question 2:  Once I can measure the arc length of a parabola, how do I go about manually changing it to a specified length (Ex: If my arc length is 14, but I need it to be 24)?  Followup question, is there a way to use a slider in Grasshopper to do this?

Question 3:  Once I eventually am able to create a parabola of a specific arc length/curve length the next thing I'll be doing is to create a parabolic cylinder comprised of 6 inch squares (view image below for visual cue).  Is there a way to change the scale of a parabolic cylinder while still maintaining the 6x6" grid/panels?  I plan on using a 3D printer to print out 6x6" interlocking tiles that when glued will form a parabola, and would like to be able to do it for a variety of parabola sizes.