I can't cut this object, I always have some errors.

I have attached the file with the various curves and surfaces to cut, and I have to cut this surface in various points to obtain a floor with wooden boards and as shown in the example attached with Moi3D this seems impossible, someone can help me.

Furthermore, on this type of surface it is practically impossible to obtain a thickness and I had to give up but now I can't even cut this element.



Here the same object that i want


and this is the screen shot of attached 3dm in the zip file attached


Thanks for any suggestion and help to solve this problem