Soak tamarind paste in 3/4 cup boiling water for about 10 minutes, then push it through a mesh strainer to remove the seeds and fibers and extract as much pulp as possible. Stir fish sauce, rice vinegar, sugar, cayenne, and 2 tablespoons oil into tamarind liquid and set aside.
Cover rice sticks with hot tap water in large bowl; soak until softened, pliable, and limp but not fully tender, about 20 minutes. Drain noodles and set aside. Beat eggs and 1/8 teaspoon salt in small bowl; set aside.
Heat 1 tablespoon oil in 12-inch skillet (preferably nonstick) over high heat until just beginning to smoke, about 2 minutes. Add shrimp and sprinkle with remaining 1/8 teaspoon salt; cook, tossing occasionally, until shrimp are opaque and browned about the edges, about 3 minutes. Transfer shrimp to plate and set aside.
Off heat, add remaining tablespoon oil to skillet and swirl to coat; add garlic and shallot, set skillet over medium heat and cook, stirring constantly, until light golden brown, about 1 1/2 minutes; add eggs to skillet and stir vigorously with wooden spoon until scrambled and barely moist, about 20 seconds. Add noodles, dried shrimp, and salted radish (if using) to eggs; toss with 2 wooden spoons to combine. Pour fish sauce mixture over noodles, increase heat to high, and cook, tossing constantly, until noodles are evenly coated. Scatter 1/4 cup peanuts, bean sprouts, all but 1/4 cup scallions, and cooked shrimp over noodles; continue to cook, tossing constantly, until noodles are tender, about 2 1/2 minutes (if not yet tender add 2 tablespoons water to skillet and continue to cook until tender).
Transfer noodles to serving platter, sprinkle with remaining scallions, 2 tablespoons peanuts, and cilantro; serve immediately, passing lime wedges separately.