In a large pot over high heat, boil 2 quarts salted water. Fill second pot with ice water; set aside. While waiting for water to boil, to a medium bowl, add and mix to combine 1 cup olive oil, vinegar, 1 teaspoon Dijon, lemon juice, and tarragon. Set aside. Finely dice celery, fennel and red onion. Set aside. Toss shrimp in boiling water. Turn off heat and let shrimp steep for 3 minutes, then strain and immediately plunge into ice water to cool. Cut into 1/4-inch pieces. Place crab, scungilli, and shrimp in a large bowl and lightly toss with celery, fennel, and red onion. Cover with vinaigrette and toss. Season with salt and pepper. Refrigerate.
Slice calamari into 1/4-inch pieces and steep in buttermilk. To make aioli, place garlic, 1 tablespoon Dijon, egg yolks, anchovies and chili in food processor and pulse while slowly streaming in 1 cup olive oil. When the mixture becomes thick and smooth, add lemon zest and 1 teaspoon black pepper. Salt, to taste, and refrigerate until ready to serve.
Combine the 2 flours in a medium bowl. Add salt and pepper, to taste. In a large Dutch oven or heavy bottomed pot, heat oil to 375 degrees F. Lightly dredge the calamari through the flour. Shake off any excess flour and place immediately in fryer. Cook until crispy and golden brown. Remove from oil and let drain on a paper towel lined plate.
To Serve: Round a serving spoonful of salad in the center of each plate. Scatter a few pieces of calamari over each scoop and top with a dollop of aioli. Garnish with baby arugula.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.