Make the broth first. Pat the pike carcass dry with paper towels and coat with a little vegetable oil. Salt it well and grill it, bake it or smoke it until it's nicely browned. While that's cooking, caramelize the onion in the stockpot. Cook the onion over medium-low heat in about 2 tablespoons of the same oil you used for the fish carcass. Take your time here, as you want the onions to be nicely browned.
NOTE: If you are making the dill oil, do this while the fish is roasting and the onions are caramelizing. Put the dill and oil into a blender and puree for a solid minute to 90 seconds -- you want the mixture to heat up a little. Set a fine-meshed strainer over a bowl and pour the puree into the strainer. Let this drain untouched while you make everything else. If you find that too many solids are passing through the mesh, restart the straining process with a paper towel set inside the mesh; the oil will soak through, the dill won't.
Once the carcass and onions are nicely browned, add the remaining broth ingredients and bring to a bare simmer. Simmer for 40 minutes to 1 hour -- no longer than that -- and then strain though a fine-meshed strainer with a paper towel set inside. You want as clear a broth as you can get, although clarity is mostly for looks, not flavor. Salt the broth to taste and keep the broth hot (but not simmering) in a pot on very low heat.
Cook the wild rice in 2 cups of the broth. True wild rice cooks quickly, but if you can only find the cultivated variety (which is what is sold in most stores), add another cup of water to the stock and cook until tender. Drain the rice but keep the cooking liquid.
Use this cooking liquid to simmer your diced root vegetables until tender but not mushy. It should not take long, as they are cut small. It should take about 8 to 15 minutes. Drain the vegetables, set them aside and again, keep the liquid.
Now use the cooking liquid to poach the pike. Add a little more broth or water if you need to. To do this, bring the liquid to a boil, drop the pike pieces in and turn off the heat. Let them poach in the hot liquid for 5 minutes. Remove with a slotted spoon.
To finish the soup, divide the rice, root vegetables and fish among your soup bowls and pour over the hot broth. Garnish with the choped celery leaves and chives and drizzle a little dill oil over each bowl. Serve at once.