Is there an actual diagnosis of emotional attachment problems?

Yes. Attachment disorder develops when children have been unable to consistently connect to parent or caregiver. The disorder ranges from 'insecure attachment' to more severe form, reactive attachment disorder. Reactive attachment disorder is common in children who have been neglected or abused, lived in orphanage, or bounced around in foster care.
Yes. Attachment disorder is a broad term that describes disorders of mood, behavior, and social skills that result in problematic social expectations and behaviors. The term attachment disorder is most often used to describe emotional and behavioral problems of young children, but is sometimes applied to school-age children or even to adults.