Combine farro, 1/4 tsp. salt and water in a medium sauce pan; bring to a boil over high heat. Reduce heat to low and simmer, covered, until farro is tender, about 20-30 minutes. During the last 3 minutes, add shrimp and continue cooking until shrimp are pink and cooked through. Drain and allow to cool slightly.
Meanwhile, in a small bowl combine dressing ingredients: yogurt, mayonnaise, vinegar, 1/2 tsp. salt and pepper.
Combine corn, zucchini, tomatoes, basil, and shallot with farro/shrimp and dressing. Cover and chill for at least 30 minutes.