Is it possible, to intentionally engineer structures, to be "nano-sharp", by manipulating the electron orbitals, on the "leading edge" of that structure ?

In the sense that you could put an atom which had a p-orbital, rather than an s-orbital, into that location, yes.

does 'sharp' matter at the atomic scale? What's the application?

Yeas sharp on an atomic scale has a very large effect in imaging. The resolution obtained from scanning tunnelling microscopy is determined on how sharp u can get the tip of microscope. The best resolution possible is obtained with a point of a single atom.