Should i exercise even though i'm underweight and don't meet the daily nutritional requirements? if so, which specific exercises should i do?

I would check this: One out with your personal physician. He or she knows the pertinent info to provide you with a meaningful answer.

Yes, exercise.: Exercise is always a healthy thing to do. Good for heart health, blood sugar and cholesterol management, and energy and vitality. Being overweight, you may want to do aerobic type exercises three or four days weekly and focus on weight training, which will build muscle and shape and bring your weight up a bit through the building of dense muscle tissue. And please try to eat better.