Well it depends on the type of nurse (inpatient, community etc) and their level of competence (ability to prescribe medication or provide therapy) so very broadly..
Provide practical and emotional support, act as an advocate, co ordinate care with other health professionals or organisations as required, monitor presentation and assess for improvement or deterioration, care plan, risk assess, provide therapy, prescribe/ administer/ review medication, monitor physical health and so on and so on.
No not everyone with this diagnosis needs a mental health nurse.