In pot over high heat, combine chicken with 5 quarts water or enough to cover. Bring to a boil, skimming foam as needed; reduce heat to medium-low. Meanwhile, cut half the carrots and parsnips into 2" pieces. Halve the remaining carrots and parsnips lengthwise. Cut into 1/2" pieces; set aside. To soup add celery, onion, garlic, and reserved large carrot and parsnip pieces; simmer 1 hour. Add next 4 ingredients; simmer about 30 minutes. Strain, reserving broth and chicken.
Discard skin from chicken. Pull meat from bones; cut or tear into bite-sized pieces. Return broth to same pot over medium heat; add remaining carrots and parsnips. Simmer until vegetables are almost tender, about 10 minutes. Add chicken; heat well, about 5 minutes. Stir in last 4 soup ingredients. Cover; set aside.
Meanwhile, in a skillet over low heat cook reserved chicken fat, stirring occasionally, until melted and solids begin to brown, 30 minutes. Strain fat, discarding solids. Measure melted fat; add enough vegetable oil to equal 1/3 cup, if necessary.
In small pot over medium heat, combine schmaltz, eggs, salt, pepper, and seltzer . Stir in matzo meal. Cover; refrigerate at least 30 minutes.
Fill skillet halfway with water or chicken broth. Place over high heat; bring to a boil. Reduce heat to medium. With lightly moistened hands, shape tablespoonfuls of matzo mixture into balls. Gently add to simmering water or broth.
Cover; simmer until all matzo balls are cooked through, about 20 minutes. using a slotted spoon transfer matzo balls to soup. Let stand 15 minutes to allow matzo balls absorb flavors of soup. Reheat, if necessary, and serve.