"Vary" is a nice business word. It means to change, like differ. So you can say, "The prices vary depending on the date."
In the second sentence, usually we would say, "We can offer a special discounted rate on your room." I know it sounds strange but we usually don't say, "my boss....can do something." If you say "we" it makes the customer feel like you care about them personally. But it is not wrong to say, "My boss (I would use manager) can offer a special discounted rate on your room."