Heat grill to high.
Cut top and bottom from watermelon. Slice remaining watermelon into 1-inch-thick vertical slabs, leaving outer peel and rind intact.
Place the watermelon slabs and halloumi slices on a rimmed baking sheet. Set aside.
In a small bowl, stir together 3 tablespoons of the lime juice, 2 tablespoons of the olive oil, 1 tablespoon of the chopped ginger and ½ teaspoon of the salt.
Pour mixture over watermelon and cheese, turning each piece to coat evenly in the marinade. Chill, uncovered, for 30 minutes.
Meanwhile, in the same small bowl, stir together shallots, honey, and remaining ¼ cup lime juice, ¼ cup olive oil, 1 tablespoon ginger and ½ teaspoon salt until combined. Let the vinaigrette stand at room temperature until ready to use.
Place the watermelon on an oiled grill grate and grill, uncovered, turning once, until grill marks appear and watermelon is slightly tender, 2 to 3 minutes per side. Transfer watermelon to a cutting board.
Place the halloumi on the grate and grill, uncovered, turning once, until grill marks appear and cheese is slightly softened, about 1 minute per side. Remove from grill and cool on wire rack, about 5 minutes.
Arrange the arugula on a large platter. Cut 2 watermelon slabs into wedges (leaving rind intact) and slice halloumi into cubes. Arrange watermelon wedges and halloumi over arugula, and spoon ¼ cup of the vinaigrette over top.
Sprinkle the salad with chopped pistachios and serve it with the remaining watermelon wedges and vinaigrette.