A Turkish van can sometimes be all white, as can Persians, Angoras, and a select few Ragdolls (with very specific mutations of the White Spotting Factor), Cornish Rex, Devon Rex, Manx, and American or British Shorthairs.
Most often you wont find an entire breed of all white cats. You'll have to search for that breed of cat in that color (weeding through other colors you don't like).
If by frisky, you mean playful, these "frisky" breeds: Siamese, Oriental Shorthair, Oriental Longhair, and the Singapura. These breeds are often considered "dog-like" because they always want to be by your side.
An American longhair is a species of large, semi-longhair domestic cat, also known as the Maine coon.
This is not a complete list of all cat breeds, just some of them: Abyssinian Australian Mist American Bobtail American Curl American Shorthair/Longhair American Wirehair Balinese Bengal Birman Bombay Brazilian British Shorthair/Longhair Burmese Chantilly/Tiffany Chartreux Cornish Rex Devon Rex Domestic Shorthair/Longhair (Moggy) Egyptian Mau Exotic Shorthair Havana Brown Japanese Bobtail Maine Coon Manx Munchkin Norwegian Forest Cat Oriental Shorthair/Longhair Persian Ragamuffin Ragdoll Russian Blue Savannah Scottish Fold Siamese Siberian Snowshoe Sphynx Tonkinese Turkish Van York Chocolate Cat
These are all the longhaired cats so I guess they are pretty fluffy American Longhair, Balinese, Birman, British Longhair, Burmilla (sometimes), Cymric, Himalayan/Colorpoint Persian, Javanese, Kurilia Ragdoll, American Bobtail, Maine Coon, Nebelung, Norwegian Forest Cat, Persian, Ragamuffin, Siberian, Somali, Turkish Angora
Breed and color are only loosely related in cats. There are certain colors associated with particular breeds, such as the Russian Blue and the Siamese, but what you've described is your basic moggy. At a guess, it's a domestic shorthair or longhair.
An Asian semi-longhair is a rare breed of domestic cat originating in Britain.
Does the cat have an "M" on its head? if so its a Mane Coon. I imagine your cat is this or an American Domestic Longhair, this are mixed cats.
The first Siamese cat in America was reportedly given to Mrs. Rutherford B. Hayes (the first lady to the nineteenth President of the United States) in 1878 by the U.S. Consul, David Stickles, living the rest of its days in the White House. In the 1900s, Siamese cats participated in various cat shows and today, occupies the top place among short haired cat breeds. Due to its popularity, the Siamese breed has been used to form many modern cat breeds including the Ocicat, Himalayan, Burmese, Tonkinese, Korat, Snowshoe, and myriad Oriental breeds (Oriental Shorthair, Oriental Longhair, Colorpoint Shorthair, Colorpoint Longhair, Balinese, and Javanese).
All breeding cats compete at regional cat shows for championship titles. Supreme Longhair Burmilla Exhibit & Best Longhair Burmilla Male Kitten.
A white cat could be one of many breeds of cat, but it is likely it is a Domestic Shorthair or Domestic Longhair. These are cats with very mixed genes and no particular breed. Domestic Shorthair or Domestic Longhaired cats can vary in terms of body shape and size. However, if the cat is indeed fat (you cannot feel its ribs under fur, and has no waist), it is likely being overfed or being fed the wrong sort of food.
A gray cat with white on its legs may either be a blue and white cat or a brown tabby and white cat. If there are no stripes, spots, or other markings on the gray color, then it is a blue and white. If there are stripes, spots, or other markings on the gray color, then the cat is a brown tabby and white. Also if it has light orange/tan marks it could be a Dilute Calico.
No, the purebred Burmese cat will not be longhaired. The cat will be short haired or semi-longhair.