General answer: No.
However, it really depends on which stage of the Atkins diet. In the primary (induction) phase, carb intake is typically limited to less than 20 grams per day (not counting fiber). A potato contains on average 26 grams of carbs MINUS 3 grams of fiber yielding 23 grams of allowable carbs which is greater than the "critical carbohydrate level" for this stage.
You can; however include starchy vegetables including potatoes in the "Ongoing Weight Loss" phase of Atkins.
No
Yes, you can eat shrimp on the Atkins diet.
Yes, you can eat the cornflakes while you are on the Atkins diet.
Absolutely. In fact eating mayonnaise (and other fatty foods like crisco and horse grease) are seriously encouraged (mandatory) in the Atkins diet. Dr. Atkins recommends that a person eat AT LEAST one cup of mayonnaise DAILY on the Atkins diet. Enjoy!!
can i eat ranch dressing
Yes, you can eat the battered onions rings on the Atkins diet.
The best Atkins diet to follow is strictly no carbohydrate. A good rule of thumb is that if a food is light in color then it has a lot of carbs in it. You should eat a lot of red meat and stay away from potatoes and noodles.
if it is meat you can eat it.
Pasta
in the first phase of the Atkins diet, you can not eat beans.
Because the Atkins diet is high protein, low carbs, you are required to purchase a lot of meat products; But you will not eat that meat in huge quantities. Meat is more expensive than veggies, potatoes and the like. The high expense comes into being with Atkins, when you purchase the Atkin's prepackaged foods. You do not need them to be on the diet, so save your money.
Atkins.com is the official website for Atkins diet information. Atkins-diet-advisor.com is also a good source of information, with a list of specific menu items you can eat on this diet.