Put the noodles in a medium bowl with hot water to cover. Soak until tender, about 30 minutes. Drain and set aside. Whisk the sugar with the fish sauce and vinegar in a small bowl.
Heat a large skillet over medium heat until hot and add 1 tablespoon of the peanut oil. Pour in the eggs, tilting the skillet as you pour to make a thin, even coating of egg. Cook until just set, about 45 seconds. Invert the eggs onto a cutting board and cut into 1/2-inch pieces. Set aside.
Add another 1 tablespoon of the peanut oil to the same skillet and heat over high heat. Add the shrimp, 1/2 teaspoon of the pepper flakes, and salt, to taste. Stir-fry until the shrimp are pink and just cooked through, about 1 1/2 minutes. Transfer to a plate.
Heat the remaining 2 tablespoons peanut oil over high heat. Add the garlic, shallots, and remaining 1/4 teaspoon red pepper flakes and stir-fry until lightly browned, about 1 minute. Add the tofu and cook about 2 minutes more. Add the noodles and cook, tossing, until lightly coated with the garlic mixture, about 1 minute. Add the fish sauce mixture and large scallion pieces and heat through. Stir in the cooked egg and shrimp, 1 cup of the sprouts, and the 1/3 cup peanuts and toss until hot. Divide the Phad Thai among plates and top with the remaining sprouts, additional peanuts, and chopped scallions. Serve immediately with the lime wedges and Sri Racha.