Preheat a grill over medium-high heat to 425 degrees.
Cut 8 sheets of 12 by 14-inch heavy-duty aluminum foil. Use two sheets of foil per packet.
To a large mixing bowl, add Zucchini, Yellow Squash, Grape Tomatoes, Green Bell Pepper, Red Onion, Fresh Corn, and Shrimp.
Drizzle over Olive Oil, then sprinkle over Garlic, 1 tsp Salt, and freshly ground black pepper, Paprika, Celery Seed, Dried Thyme, and Cayenne Pepper.
Toss mixture well to evenly coat.
Layer two sheets of foil per packet, with the first sheet of foil laying in opposite direction of the second. Divide mixture among double lined foil adding it to the center in a rectangular shape.
Wrap up sides of first sheet of foil and roll edges several times to seal, then place second sheet going opposite length and wrap while rolling edges to seal.
Grill until Shrimp is cooked through, about 12 to 14 minutes, while flipping packets over to the opposite side once halfway through grilling.
Carefully open packets as steam will escape. Sprinkle with Parsley and serve with Lemon Wedges for spritzing.