Beginner to Rhino and Grasshopper and hoping you all can help me with my modeling predicament. I have two curves between which I would like to place a series of connecting lines. (Please see attached sketch.)

make the two curves, divide them in equal amount of points, and feed these to a line component to start with. If this makes no sense to you, then I highly recommend to take the first steps in going through the grasshopper 101 tutorial. You can find it on grasshopper3d.com

The problem is that I would like the points along the two curves to be at different intervals (therefor different amounts of points). I am therefor having problems getting the line to connect to the correct points, rather than bunching up at the first point.

this makes no sense, for each line you need 2 points. If you need more control over where the points go, you might need to divide it into subcurves of different lengths

Okay, understood. Is there any way to control the distance between the points using something like a sine wave? I would like for the points to bunch up in waves. Please see sketch below.

you could draw a sine curve, divide that, then project these back onto the line

there are several ways to accomplish this, but if it is just a simple box, you could draw a box and scale it to the lengths of your curve (by scaling and mapping from plane to plane)
Another way: offset each line, offset both sides, then loft, then extrude the resulting surface

This is fantastic - thank you very much for spending time on this and sending it over! It was very helpful. What I’m still a little confused on is where your original geometry is coming from. When I try to insert some of your coding into my model it doesn’t accept my lines as the original geometry (see below).