Place garlic cloves, 1/4 cup olive oil, key lime juice, rosemary, and 1/2 teaspoon garlic salt into a blender; puree until smooth. Combine shrimp and marinade in a resealable plastic bag. Marinate at least 30 minutes in the refrigerator.
Place an oven rack in the topmost position and preheat oven on the broil setting.
Pour the shrimp and their marinade onto a baking sheet lined with aluminum foil. Broil in preheated oven 3 to 4 minutes per side until the shrimp are opaque. Once cooked, pour everything into a bowl and place into refrigerator.
Meanwhile, bring a large pot of lightly salted water to a boil. Add green beans and cook for 2 to 3 minutes, until tender; drain and rinse with cold water. Drain excess water from the chilled beans and place into a large bowl.
Heat remaining 1/4 cup olive oil in a large skillet over medium heat. Stir in minced garlic and onion, cook until the onion has softened and turned translucent. Pour the oil over the beans, add shrimp mixture, and toss. Season with garlic salt, and pepper; mix well. Cover and refrigerate at least 1 hour. Mix in crumbled feta before serving.