Immunizations for school

A mother brings her 12-year-old daughter to the clinic to establish care and to get immunizations for school.  Her mother reports that because of lack of insurance she has not had a regular pediatrician for her children for the previous eight years. She reports the girl to be in general good health other than recurrent bouts of the otitis media. The mother is concerned that she and her other two daughters began their growth spurts and their menstrual cycles by age 11 years, but this child “hasn’t got her period.”  The child reports that she is doing well in school except for mathematics and she requires help with attention in planning in school activities. On physical examination, she is at the 5  th percentile for height and the 90  th percentile for weight.  She is afebrile, heart rate 90 bpm, respiratory rate 16 breaths/min, and BP 117/92 mm Hg. Her chest is broad and her femoral pulses diminished.

-What is the most likely diagnosis?
-What are the most appropriate diagnostic test to order?
-What is the best management for this condition?
-What is the genetic basis of this disorder?