Preheat oven to 400°F. Place each beet on a separate 12-inch square of aluminum foil. Drizzle beets with 1 tablespoon olive oil; sprinkle with ½ teaspoon salt. Fold foil sheets around each beet, and crimp tightly to form 2 airtight packets. Place packets on a small baking sheet, and roast in preheated oven until beets are tender but not mushy, 1 hour to 1 hour and 30 minutes. Remove from oven. Let beets cool in sealed packets 30 minutes. Unwrap cooled beets and peel. Cut beets into ½-inch wedges. Set aside.

While beets roast, trim ¼ inch from top and bottom of each citrus fruit. Stand each citrus fruit upright on trimmed bottom; using a sharp knife and following the curve of the fruit, cut and remove the rind and white pith. Slice citrus crosswise into ¼-inch rounds, and halve rounds into half-moons. Alternatively, slice in between membranes to cut into supremes. Set citrus aside. Squeeze juice from rinds into a small bowl to yield 1 tablespoon juice. Add lime juice, honey, mustard, pepper, ½ teaspoon salt, and remaining ¼ cup olive oil; whisk until well combined. Set aside.

Pour vegetable oil to a depth of 1 ½ inches in a medium saucepan, and heat over medium-high until oil reaches 400°F. Stir together flour and remaining ¼ teaspoon salt in a medium bowl. Toss halloumi cubes and 1 tablespoon water in a separate medium bowl; drain. Add halloumi to flour mixture, and toss well to coat; shake off excess flour mixture. Working in batches, fry halloumi, stirring occasionally, until crispy and dark golden brown, 1 minute and 30 seconds to 2 minutes and 30 seconds per batch. Using a slotted spoon, transfer halloumi to a paper towel–lined plate.

Arrange arugula, beet wedges, and citrus on a large platter; drizzle with ¼ cup dressing. Top salad with halloumi croutons, pomegranate arils, and pine nuts. Serve with remaining dressing.