If someone is not sick, is she healthy?

Not necessarily. 

There are three parts to health: physical health, mental and emotional health, and social health.

Sickness is part of the physical health.

She could have terrible relationships with other people, therefore not being healthy in the social health section of the triangle, or not get good grades, therefore not being healthy in the mental/emotional side of the triangle.

Because without physical activity, the body has extra "energy" if you will, and so when it is time for bed you are not tired, so you end up staying up all night. also there is probably an effect on your internal clock, which messes with your melatonin production which goes hand in hand with your sleep cycle