Yup u need to lose weight its little bit high almost 10 lbs my sis is 5'2 and she is 100 pounds I would prefer u to diet and do running u would loose 10 lbs very easily though if your weight don't burn off then tell me either way I think running will help u you don't need to do any exercise if u think you're perfect
Concentrate on getting more toned than losing weight. Ur weight is ideal so I wouldn't worry much. Pick up some weights :)
Your bmi is 20.7 that's 2 points above what would be underweight for you.
You wouldn't want to lose to much. I think maybe some muscle toning exercises will suite better.
And don't forget clean eating too. Would be better to be healthy and fit than hungry and skinny.
Just muscle exercices and some cardio that tell the body to burn fat