Hello! I'm glad to see you're interested in the game.
Yes, the Powers that Forsworn get alongside their Oaths are just like in the Mystic's playbook; they allow you to cast spells and rituals by borrowing your patron's powers and spending playbook points.
While a player could pick the "add +1, once or more per roll" that Mystics get by default, it would be fairly redundant as each playbook natively gets the ability to spend a point to add +1 to a roll (with narrative grounds to do so). One would gain the ability to do this multiple times per roll, burning through several points in doing so; if that's something that the player values, then it wouldn't be totally useless.
Your character keeper seems great so far!