The 0% deal does already include the interest on the price of the car, but if you are getting finance then the amount you pay overall will 9 times out of 10 be less on the 0% deal.
It's a fallacy that you will be able to haggle more by paying 'cash in hand', the dealership get's a commission if they sell you a finance agreement (along with the overpriced gap insurance, extended warranty etc..) which is usually just as valuable to them as the profit they make just on the car.
The best time to buy a car isn't at the end of the month, it's when they have enough time to order the car and get it handed over to you before the end of the quarter. It only registers as a sale to the car manufacturer once the car is handed over, and the dealership doesn't get it's commission until that has happened. They get tiny commissions on brand new cars though, with the big commissions only coming if they hit set targets (and therefore handovers) by the manufacturer.
If you walk into a dealership the day before the end of the quarter, they won't give you much time as they'll be wanting to hand over all the cars they currently have waiting to take delivery so they hit their target they are one or two cars behind on.