Preheat oven to 325°F, and line a baking sheet with parchment paper. Add pita to prepared baking sheet, and drizzle with 2 1/2 tablespoons oil. Sprinkle with sumac and 1/4 teaspoon salt, and toss until evenly coated. Bake in preheated oven until pita is light golden in spots, 10 to 12 minutes, stirring halfway through bake time. Remove pita from oven, and set aside until ready to use. (Pita chips will continue to crisp as they cool.)

Meanwhile, combine crumbled feta, yogurt, and 2 tablespoons oil in a blender; process on low speed, gradually increasing speed to medium, until mixture is smooth, about 1 minute. Set aside until ready to serve. Wipe blender clean.

Add cilantro, parsley, lemon juice, vinegar, 1/4 teaspoon salt, and remaining 6 tablespoons oil to blender; process on low speed, gradually increasing speed to medium-high, until dressing is smooth, about 1 minute. Set aside.

Gently toss together arugula, celery, fennel, pine nuts, 1 cup pita chips, 2 tablespoons cilantro-parsley dressing, and remaining 1/4 teaspoon salt in a large bowl until coated.

Divide and spread reserved feta mixture evenly over 4 plates. Top each plate with celery salad, and spoon remaining dressing evenly over salad. Top with remaining pita chips, and garnish with additional sumac.