layer via cut/copy is modifying the layer

I merge all the layers first , then make selection and make layer via copy .

What Selection and why? 

To duplicate a Layer no Selection is needed and re-applying a Layer’s transparency naturally will have an effect (unless the pixels’ transparency is strictly either 0% or 100%). 

Could you please post screenshots with the pertinent Panels (Toolbar, Layers, Options Bar, …) visible taken at View > 100%? 

"I'm trying to copy layers precisely the way they are."

Are you really? In that case you could Alt/Option + drag a layer to copy it. Content should be identical.

You also don't need to merge layers to copy from it as if it was merged. Make a selection, then Shift + Ctrl + C to Copy Merged. Paste in Place (Shift + Ctrl + V) can put it on a new layer in the same spot.

Not sure what you did here, but maybe it helps.

I think thats anti-aliasing that you can not skip when selected curved lines because curved lines are crosing pixels. Pixel can not be divided on half or third, it actually can not be divided at all. Either you will have anti-aliasing or pixelated, jagged edge look without anti-aliasing. 

What is actually anti-aliasing? In short,  if your selection line is crossing pixel at half, anti aliasing will reduce opacity of that pixel to 50%. If selection curved line is crossing pixel at one third, opacity will be lovered to... guess what opacity?