For the cioppino: Preheat the grill to medium-high heat. Wipe down the grates with an oil-blotted towel to clean and create a nonstick surface.
Squeeze the lemon halves (catching the seeds and discarding) into a large bowl, then add the lemon halves to the bowl as well. Add the wine, olive oil, capers, salt, chile flakes, peppers and garlic. Whisk to combine and set aside.
Clean and cut the crabs: remove the hard shell, cut off the tail and discard the gills, then cut the halves into pieces so each piece has 2 to 3 legs. Place the crabs, scallops, shrimp and halibut in the marinade and gently toss to coat. Cover and refrigerate for 1 hour, giving it a stir after 30 minutes.
For the puree: Place the tomatoes, bell peppers, fennel and onions in a large gratin dish, and then drizzle with three tablespoons of the olive oil, 2 teaspoons salt and 1/2 teaspoon pepper. Add the fennel seeds and chile flakes and toss to coat everything evenly. Cut the top off of the bulb of garlic to expose the cloves. Place the garlic on a large piece of foil and drizzle with the remaining 1 tablespoon olive oil and sprinkle with a pinch each salt and pepper. Wrap up the foil into a tight pouch. Place the vegetables on the grill and the garlic pouch in the corner of the grill over indirect heat. Grill the vegetables on both sides until tender and charred around the edges, 8 to 10 minutes. Remove the vegetables and set aside. Roast the garlic over direct heat until medium brown and paste-like, 20 to 25 minutes. Remove from the grill, cool enough to handle, then squeeze out the garlic paste from the bulb and set aside. Working in batches, add the vegetables and garlic paste to the bowl of a food processor and pulse until sauce-like in appearance and consistency. Transfer to a large saute pan set over medium heat. Stir and simmer until the sauce slightly thickens, 7 to 8 minutes. Add half of the basil and the ouzo, then remove from the heat and set aside.
Grill the crab for 4 to 5 minutes, then flip and cook for another 3 to 4 minutes. Grill the shrimp for 3 to 4 minutes then flip and cook for 2 to 3 minutes more. Finally add the halibut and scallops to the grill; cook for 2 to 3 minutes on the first side then turn over and cook for 2 to 3 more minutes. Remove all the seafood from the grill to a platter.
Serve the seafood family-style with the sauce generously ladled on top. Garnish with the remaining basil, the quartered lemons and the reserved fennel fronds.