Can type 2 diabetes be managed through nutrition and exercise?

Absolutely. The severity of diabetes can vary widely. If your blood sugars or only mildy elevated, then a regimen of exercise, weight loss and diabetic diet can absolutely get things under control. Talk to your doctor and a diabetic dietitian. Good luck!
Sometimes. Type 2 diabetes can respond to an ada (american diabetes association) diet and vigorous exercise to the point where medications may not be needed. This is not typical but can occur in some cases. Nonetheless, good nutrition and exercise are still very important in diabetes as it can result in needing less medication and it certainly improves your cardiovascular health.
It's possible. Technically we can't "cure" diabetes, but we can control it with strict diet (low fat, low cholesterol, upwards of 50 grams of fiber daily, small meals five or six times daily), exercise (aerobic) and weight reduction. However, I wouldn't usually recommend this without medication to patients with blood sugar values above 160.
Yes. Absolutely! That is the primary treatment for all diabetes type 2 cases. Medications won't fix the problem if you don't control your diet, get proper measured nutrition, and do some form of physical activity. The main problems with diabetes are blood pressure, cholesterol, fats, and sugar - all managed by diet and exercise. Many patients end up going off diabetes meds entirely.