Eileen's main characteristic is stubborness which is great for giving her the necessary drive and determination to defeat monsters as she simply won't give up. That same trait makes relationships unnecessarily complicated for Eileen as she upsets people when she doesn't have to (but that's what makes her a fun character to write for. I like dropping my characters in it! Or better still using their traits to get them to drop themselves in it and Eileen does this wonderfully well!).
Eileen also cares passionately about justice which of course generates an immediate conflict with the criminally minded. Also it can cause conflicts with the Queen and her Council given definitions of what makes up justice can vary.
Brankaresh cares only about power and wants to be the most powerful wizard the Fairy Kingdom has ever seen. This is not an ambition that is going to go down well (especially with Eileen) so he has to disguise this. So something a character cares about can be suppressed or disguised and you generate the immediate conflict as to how well can that character do this? Will it all go horribly wrong so the disguise falls apart and how would other characters react to that? Equally will that character keep the disguise up brilliantly and fool everybody? What will the consequences be?
So to give your stories and characters bite, make them care about something. Really care. The be prepared to make sacrifices for type of caring.