For the fish stock: Place 1 gallon of cold water and the fish tails, fins, heads, bones and skin in a large, wide saucepan with a cover. Bring the water to a boil, and then lower it to medium-high heat. Remove the foam that accumulates. Add the carrots, onions and celery to the water, followed by the salt and sugar. Cover the saucepan and simmer the stock for about 20 minutes while preparing the fish mixture.
For the fish mixture: Place the ground pike and whitefish together onto a large cutting board. Process the eggs, carrots and onions in a food processor until the mixture becomes finely whipped. Add this mixture a cup at a time to the ground fish by chopping it in with a cleaver until it is all incorporated together.
Put the fish mixture in a large bowl, and then alternate adding some of the cold water and matzah meal until you achieve a light, soft texture. When you have incorporated about two-thirds of the water and matzah meal, add the salt, some pepper and some sugar.
Wet your hands in cold water and form the fish mixture into oval shapes, about 3 inches long each. Turn down the fish stock to a low heat and remove the fish tails, fins, bones and skin. Gently place the fish ovals in the fish stock and cover loosely, simmering for about 1 hour. Remove the cover and taste the liquid while the fish is cooking and add pepper and sugar to taste.
When the gefilte fish is cooked, take the saucepan off the heat and let the fish cool inside until the ovals are cool enough to remove by hand. Gently remove each oval from the water along with the whole carrot. Place the gefilte fish ovals on a plate and slice the cooked carrot into rounds 1/4-inch thick. Place a carrot round on top of each piece of gefilte fish and place in the refrigerator to cool overnight.
Strain the fish stock and boil it until it has reduced by half. Chill the stock in the refrigerator until you're ready to serve. Serve the gefilte fish with some of the stock and Fresh Horseradish and Beet Relish on the side.
In a large bowl, add the horseradish, beet, vinegar and sugar, and mix thoroughly. Season with salt and pepper. Let the mixture sit in the refrigerator for 24 hours before serving.