Can I lose 10 lbs for two months with a balanced diet and 30 minutes exercise daily?

Yes, but you will also have to cut out at least 500kcal from your dietary intake each day. Safer is about 8 pounds in 8 weeks.
Sure. That would be a prudent amount of weight to lose. Ten pounds would be 35,000 calories; divided by sixty days would be a daily caloric deficit of 583 calories. So cut your daily intake by 583 calories or exercise for 583 calories daily and you'll lose that weight. As long as you create this caloric deficit you should lose your weight on time.