In advertising, is the money allocated for coupons taken directly out of the entire advertising budget?

I am assuming that you are asking if the costs associated with creating and publishing the ads will be accounted for through the advertising budget, and that is correct. The fact that some companies mark-up their prices prior to sales is irrelevant to the way these coupon costs are accounted for. Coupons are a form of advertising because their main purpose is to entice customers into making a purchase, and the fact that they offer a discount means very little.

This depends on the agreement between the agency and the retailer. Often, the money allocated for such is assumed by the client, not the ad agency. What you have to do is explain why it will actually make them more money by offering rebates and incentives. Some will suggest a higher price on other items, some will raise the price of the item on which you are offering the discount. Consumers will, generally, buy an item for 30% off even if it is marked up 40% because it looks like a "deal". Your answer - it is all one budget. What you lose on one end must be made up somewhere else. It's a zero sum game.