I would say "The prices differ depending on the date." and "My boss can offer a special discount for you."

The price differs(or varies) depending on the date. My boos can offer you a special price(or discount). My boss can offer a room at a special(or discounted)price (or rate).

Pretty close. The sentences should read like this: "The price differs depending on the date" "My boss can offer a special discounted price for you" "My boss can offer a room for a special price"

"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."