Cook orzo in a large pot of boiling salted water until tender, but still firm to bite, stirring occasionally. Drain. Rinse with cold water; drain well. Transfer to a large bowl and toss with 1 tablespoon olive oil.
Prepare barbeque on medium-high heat. Whisk 2 tablespoon oil and 2 tablespoons vinegar in small bowl. Brush zucchini and bell pepper with oil mixture, then sprinkle with salt and pepper.
Whisk pesto, lime juice, remaining 3 1/2 tablepoons oil and remaining 2 tablespoon vinegar in small bowl for pesto vinaigrette.
Place shrimp in medium bowl. Add 2 tablespoons pesto vinaigrette; toss to coat.
Grill zucchini and bell pepper until crisp tender, about 3 minutes per side for zucchini and 4 minutes per side for bell pepper. Transfer to work surface.
Sprinkle shrimp with salt and pepper; grill until charred and cooked through, 2-3 minutes per side.
Place shrimp in bowl with orzo.
Chop zucchini and bell pepper; add to bowl with orzo.
Add remaining vinaigrette, tomatoes, sliced basil, and mozzarella; toss to combine. Season to taste with salt and pepper.
Can be made 2 hours ahead. Cover and chill. Garnish with basil sprigs and serve cold or at room temperature.