I've been seeing these terms around and what do they stand for? Where can I obtain item schemes? Is it through exploring? And what about genetic power?

Schemes and blueprints are like recipes. You collect them, add them to your library and then you can craft (or build) them using materials. See Manor tab -> Craft and construction.

You can find them while exploring (Scriptorium buildings, treasure chests behind monsters), and sometimes beasts will return from quests with them. Or you can obtain them through trades with other players.

"Genetic power" is like pedigree, a sign of quality breeding in a beast. There's an explanation here: https://beastkeeper.com/thread/10847

Hope that helps!

Thank you for your reply, I have a better sense of it now. :)