Into a large saucepan of salted boiling water stir rice and boil 10 minutes.
Drain rice in a colander and rinse. Set colander over a kettle of boiling water (rice should not touch water) and steam rice, covered with a kitchen towel and lid, until fluffy and dry, 10 to 15 minutes (check water level in kettle occasionally, adding water if necessary).
While rice is steaming, in a small saucepan bring 1/4 cup vinegar to a boil with sugar and salt, stirring until sugar is dissolved, and remove from heat.
In a dry small skillet toast sesame seeds over moderate heat, stirring, until golden and fragrant and transfer to a small bowl.
Transfer rice to a large bowl and stir in vinegar mixture.
Cool rice and stir in sesame seeds, remaining 3 tablespoons vinegar, oil, ginger, scallions, carrot, and cucumber.
Salad may be prepared up to this point 1 day ahead and chilled,covered. Bring salad to room temperature before proceeding.
Dry-roast nori, 1 sheet at a time, directly above moderate heat (gas or electric burner), holding it at opposite corners and moving it back and forth, until it turns bright green, 30 seconds to 1 minute. With scissors cut nori into thin 2-inch-long strips.
Peel and pit avocado. Quarter avocado and cut crosswise into thin slices. Add avocado to salad with surimi if using and two thirds of nori strips and toss well.
In a small bowl stir wasabi powder into hot water and stir in cold water, soy sauce, and ginger juice.
Serve salad sprinkled with remaining nori strips and drizzled with dressing.