Breeding and traits
Nothing about breeding costs, inheritance odds, or trait grading exists. This page states what the systems are, not what they cost or how they are weighted, because that second part is not something this wiki can answer honestly.
Community take
Everything below is drawn from third-party guide sites, not verified game data. No exact numbers are given because none can be verified.
Traits. Guides describe a permanent per-Palmon modifier system, up to four traits per Palmon, graded on a scale from S down to C, and treated by players as more decisive to a Palmon’s strength than its base rarity or level. Traits are described as inheritable through breeding.
Breeding. A Nursery building is where breeding happens. Guide sites frame breeding as the way players chase specific trait combinations rather than new species, but none of the mechanics (odds, costs, or which combinations are possible) are stated consistently enough across sources, or verifiable against the client, for this wiki to repeat as fact.
If you are looking for exact odds or a trait tier list, see Reference for why this wiki does not publish that kind of content.