Slaying Edge into Slaying Edge+?

Slaying Edge evolves into Slaying Edge+, which can then be refined to, for example, Slaying Edge+ (+def).

If you inherit Killing Edge, then you'd need to use Stones to make it into Slaying Edge, and then use more stones to refine it to one of the stat increases.

So it's better to inherit a Slaying Edge to use up less Refining Stones, but refining Killing Edge is still possible.

You need to inherit Slaying Edge+ from a 5-Star unit, or inherit Killing Edge+ (still from a 5-Star unit) and refine that to Slaying Edge+. I don't think it is possible to inherit a Slaying Edge from a 4-Star unit, then refine it to Slaying Edge+.

You need Killing Edge+. That kind of evolving as you mentioned doesn't exist in FEH.
(Or fodder off a Saber for Slaying Edge+)