Adi probably does have some, or at least, she SHOULD, considering everything she goes through. She wasn't born with any hereditary or congenital mental disorders, but her own life experiences would be enough to traumatize anyone. She probably is (or will be, over the course of the story) dealing with depression, low self-esteem, PTSD, trust issues, and a serious fear of getting emotionally close to anyone.
Koreal is based heavily on his creator, who has both ADHD and probably autism (undiagnosed but suspected), and shares some of those traits, although not all of them. Thanks to story events, he's probably also going to be dealing with abandonment issues and severe loneliness.