Right and correctly are mostly synonymous. However, I would usually say: - If I understand you correctly, you mean ... - If I understand correctly, you're saying ... - (saying back to them what they said first) Is that right? Is that what you meant? "Both your orders" and "both of your orders" are commonly used. I think perhaps the second one is more grammatically correct. Your both orders is wrong.

1. Do I understand you correctly that... 2. Both of your orders.