Questions on energy oddities

To make things such as rotamer packing efficient, most terms of the standard Rosetta energy function have a maximum distance above which they have non-zero energies. Residues pairs which don’t have any atoms within that cutoff have zero interaction energy – by definition. (The functional form of the energy terms are adjusted such that the energy and the derivative smoothly transition to zero – there isn’t any sharp transition point.) The exact cutoff is term dependent, but normally is sitting somewhere around 6 Ang.

That’s probably what you’re seeing. The rotamer pair which you’re observing is probably just at the edge of that cutoff, so some conformers dip within it and have a small, non-zero energy, whereas the others stay totally outside it, resulting in an exactly zero energy.

For 2), that’s the behavior I would expect for interaction between the lysine side chain and the tyrosine backbone. If the tyrosine sidechain is entirely outside the cutoff, changing the atom positions there wouldn’t change the energy at all. But changing the lysine sidechain would change how it interacts with the backbone, and you would see an energy change.