Make rice: Rinse rice in a fine-mesh sieve until water runs clear. Drain well and transfer to a small saucepan. Add 1¼ cups water and a pinch of salt and bring to a boil. Cover and cook over low heat until water is absorbed and rice is plump, about 16 minutes. Keep covered until ready to serve.
Prep ingredients: Peel carrots and grate on large holes of box grater. In a small bowl, cover edamame with hot water and let stand 5 minutes. Trim ends from scallions and thinly slice on the diagonal; reserve dark green slices for Step 6. Thinly slice cucumbers into rounds. Peel and finely grate 1 teaspoon ginger (reserve the rest for your own use).
Make dressing: In a medium bowl, combine rice vinegar, 1 tablespoon oil, 1 tablespoon sugar, and 1 tablespoon salt.
Make salads: In a medium bowl, combine carrots, edamame, light green and white sliced scallion, ginger, and 3 tablespoons dressing, and season to taste with salt. In a small bowl, combine cucumbers with 2 tablespoons dressing and season to taste with salt.
Cook fish: Heat 2 teaspoons oil in nonstick skillet over high. Add fish, skin-side down, and cook until skin is crisp and fish is nearly cooked, about 4 minutes. Season top of fish with a pinch of salt. Flip and cook until done, about 1 minute. Transfer fish to cutting board, skin-side-down. Brush top of fish fillets with teriyaki sauce.
Serve: Pour remaining dressing over rice and stir until absorbed. Cut fish into ½-inch cubes; drizzle with remaining teriyaki sauce. Spoon rice into 4 bowls. Making individual piles, top with fish, carrot-edamame salad, and cucumber salad (drizzle with any remaining dressing from the bowl over the rice). Garnish with reserved scallion greens.