Follow Path Constrain to path Mesh object baffling me

blendquestionFace.blend (664.8 KB)
This objects I have made with the curves on the top. I cant do much of anything with it. I want to make it follow the path but I get an error. I want to fill it and it just makes a mess.
Any suggestions for me. I dont know how to make faces on this object so I can UV unwrap it.
I was wondering if I could take a cylinder and then use the invirse of this object to extract it bolean style
What I am after is a cylinder with a wavy top

blendquestionFace2.blend (143.8 KB)

Ok here is what I meantbOOLEANPROBLEM .blend (2.5 MB)

I tried to use this object as a cutting object. I made a cylinder 16" x 20 high then I used the object to cut the top off a cylinder off but it left a mess.
I did run all the things
" I’m applying the scales, removing doubles, recalculating normals, making them manifold by filling the gaps. After those I added boolean modifier with the help of Bool Tool that comes with Blender, it’s the one that adds the shown modifier with ctrl+np_-."
There is something blender does not like about this as a boolean.

I am missing fundamentals about what it required for Boolean to work.