Whisk first 5 ingredients in large bowl to blend. DO AHEAD Dressing can be prepared 2 hours ahead. Let stand at room temperature.
Place noodles in another large bowl. Cover with boiling water. Let stand until softened, about 4 minutes. Drain and rinse under cold water to cool; drain well. Insert scissors into noodles; cut several times. Transfer to bowl with dressing.
Add tomatoes and all remaining ingredients, except peanuts and lime wedges, to noodles; toss to coat.
Divide among 6 plates. Sprinkle with peanuts; garnish with lime wedges.