Preheat a deep-fryer or a deep pot filled halfway with oil to 375 degrees F.
Whisk together the flour, 1 teaspoon salt, 1/2 teaspoon pepper, and beer in a large bowl. Set aside for 10 minutes. Fold in the eggs. Batter should be thin.
Preheat oven to 300 degrees F.
Season the fish with salt and pepper. Dredge fish in the additional flour, tap off the excess, and then dip the fish in the batter to coat. Fry in batches until golden brown on both sides. Remove with a slotted spoon to a plate lined with paper towels. Transfer to a baking sheet and keep warm in the oven. Serve with Serrano Vinegar drizzled over top, Spicy Chips on the side, and Lemon-Habanero Tartar Sauce for dipping.
Bring vinegar to a simmer in small saucepan. Add the chiles and salt, remove from the heat, and transfer to a glass bottle or jar. Let sit at room temperature for at least 8 hours. Strain.
Place the potato slices in a bowl of cold water. Let stand 15 minutes. Drain, rinse under cold water, and drain again. Pat dry with paper towels.
Heat enough oil to come 4 inches up the sides of a large deep saucepan to 370 degrees F.
Mix together the salt, ancho powder, and chile de arbol powder together in a bowl.
Add the potatoes to the hot oil in batches and cook until golden brown, about 4 minutes. Remove from the pan with a slotted spoon, drain on paper towels, and immediately season each batch with some of the spice mixture and some of the chopped cilantro. Serve hot.
Bring the lemon juice to a boil over high heat in a small saucepan and cook until reduced to 1/2 cup. Let cool.
Combine about 2 tablespoons of the cooled reduced lemon juice, mayonnaise, anchovies, habanero, cornichons, and capers in a medium bowl. Season with salt and pepper, to taste. Add more lemon juice, to taste, if desired. Cover and refrigerate for at least 1 hour before serving.