Build a medium-heat fire in a charcoal grill, or heat a gas grill to medium. (Alternatively, heat a cast-iron grill pan over medium-high.)
For the King Crab Legs: Grill legs, turning as needed, until shells are charred and crabmeat is heated through, about 8 minutes. Serve with Seaweed Butter.
For the Lobsters and Langoustines: Bring a large pot of salted water to a boil; cook live lobsters for 5 minutes. Split each lobster in half lengthwise through head and tail. Scoop out and discard the tomalleys. Split langoustines in half lengthwise. Season lobsters and langoustines with salt and pepper and grill flesh-side down until slightly charred, 2–3 minutes for lobster and 1 minute for langoustines. Turn each over and, using a spoon, spread with Seaweed Butter; continue grilling until meat is tender, 3–5 minutes more for lobsters and 1–2 minutes more for langoustines.
For the Clams and Mussels: Grill, turning once, until shells open, about 10–12 minutes for clams and 3–5 minutes for mussels. Transfer to a bowl and toss with Chile Sauce.
For the Scallops: Grill on the half shell, flesh-side down, until browned and partly cooked through, about 3 minutes. Turn over and add 1 tbsp. Coffee Butter; grill until cooked through, basting with butter, about 2 minutes more.