Whisk the garlic, ginger, sesame oil, vinegar, soy sauce and sugar in a large bowl. Transfer 2 tablespoons of the dressing to a medium bowl, add the shrimp and toss. Add the carrot, celery and snow peas to the remaining dressing and toss.
Heat a large skillet over high heat and add 2 teaspoons vegetable oil. Add the shrimp and stir-fry until they turn pink, 3 to 4 minutes, then transfer to the bowl with the vegetables. Add 3 to 4 tablespoons water to the skillet and scrape up the browned bits with a wooden spoon, then add the liquid to the bowl with the shrimp. Let the skillet reheat, then add the remaining 1 teaspoon vegetable oil and stir-fry the rice until toasted, about 2 minutes. Remove from the heat and let cool.
Add the rice and scallions to the shrimp-vegetable mixture and toss. Divide among bowls and top with the lettuce, sprouts, chow mein noodles and/or peanuts.