Merge a group of paths or keep as separate layers?

I have created an icon that is a group of paths which I have imported from illustrator (see attached image of "0" with "/" going through center). Once I have imported into After Effects it becomes of layer with a group of paths, fills and other sub-layers (see attached layer screenshot).

first off, why did you convert it to shape? unless you plan to use shape operators or manipulate the path of the shape itself or need it to be embedded in the project with no source files - it's an unnecessary step.

My ultimate goal is to animate this layer along a path. I have tried merging, however, it does not allow me to animate along a separate desired path line.

if you want to animate a layer along the path, create a new shape layer, draw a path, then copy paste the path property to the target layer's position. this will convert the path to position keyframes. this is option 1.

option 2, can create a dynamic path. add a shape layer and create a path, then highlight the path property, then use the window->create nulls from paths, and click trace path. this will create a null that will move along the path, and defaults to loop (you can change it in the effect controls). now parent anything to that null and it will move along with it.

Are talking about simply animating the position of this layer?  Just animate its Position property.  Done.