Soak the skewers in water for at least 30 minutes. Preheat the grill to 375 degrees F or preheat a large grill pan over medium heat. Clean and oil the grates or grill pan.
Combine the lemon zest with the 2 tablespoons grapeseed oil, the cumin, turmeric, salt, garlic powder and pepper in a medium bowl; stir together. Add the chicken and toss to coat. Let sit for 5 minutes to 1 hour, then thread 5 to 6 chicken cubes onto each skewer.
While the chicken marinates, peel the cucumber into long ribbons with a vegetable peeler. Transfer to a small bowl. Add the dill fronds, the juice from 1/2 of the zested lemon and a sprinkle of salt and pepper. Toss and set aside until ready to serve.
Grill the skewers, turning every 3 to 4 minutes, until the chicken is cooked through and all sides are charred, 8 to 10 minutes total. Remove to a platter and squeeze juice from the remaining 1/2 lemon over the top.
Two minutes before the chicken is done cooking, grill the halloumi until warmed through and lightly charred, about 1 minute per side.
For each serving, top 1 pita with some of the cucumber salad, 1 to 2 slices of the halloumi and 2 chicken skewers. Drizzle with tahini and serve.