Toss the basil, dill and chives in a small bowl. Whisk the mayonnaise with half the serrano, the lemon zest, lemon juice, 1 grated garlic clove, 1/2 teaspoon salt and 2 tablespoons water in a medium bowl. Stir in 2/3 cup of the herbs (set aside the rest for topping). Cover and refrigerate.
Using kitchen shears, cut along the outer curve of the shrimp shells from the head end to 1/4 inch from the tail. Remove the top vein and rinse the shrimp under cold water (leave the shrimp in their shells). Transfer to a large bowl and add 6 cups cold water, 3 tablespoons salt and the sugar; stir. Cover and refrigerate 1 hour. Put the clams in a separate bowl, add enough cold water to cover and stir in 1/4 cup salt; cover and refrigerate 1 hour.
Preheat a grill to medium high. Toss the potatoes with 1/4 cup olive oil, 1 tablespoon salt and 1 teaspoon pepper in a medium bowl. Place the potatoes in a single layer in the center of a large sheet of heavy-duty foil. Wrap and seal into a packet, then wrap in another piece of foil to cover the seam side. Grill, flipping, until the potatoes are charred and tender, about 20 minutes per side. Keep wrapped.
Meanwhile, set aside a 4-inch piece of sausage for the clams. Grill the remaining sausage until charred, 4 to 6 minutes per side. Let cool, then cut into 3-inch pieces; cover to keep warm. Grill the corn, turning, until charred, 8 to 10 minutes. Let cool, then cut each ear in half crosswise. Drain the shrimp and grill in batches until lightly charred, 1 to 1 1/2 minutes per side. Toss the corn and shrimp with the melted butter and the remaining grated garlic clove. Cover and set aside.
Drain and rinse the clams. Slice the reserved sausage 1/4 inch thick. Heat the remaining 1/4 cup olive oil in a 12-inch cast-iron skillet on the grill. Add the sliced sausage and cook, tossing, until just starting to brown, about 5 minutes. Add the fennel, shallots and the remaining serrano and cook, stirring, until soft, about 5 minutes. Add the 4 sliced garlic cloves and the tomato paste and cook until the tomato paste turns brick red, about 1 minute. Add the wine and cook until reduced by half, about 5 minutes. Add the clams, cover and cook until all the clams have opened, 5 to 10 minutes. (Discard any unopened clams.)
Combine the corn, shrimp, grilled sausage and potatoes on a large platter. Leave the clams in the skillet. Serve with lemon wedges, the reserved herbs and the herbed mayonnaise.