Place fennel in a large bowl. Pour red-wine vinegar, 2 tablespoons olive oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper over it; stir to combine. Set aside to marinate for about 20 minutes.
In a small saute pan over medium-high heat, toast fennel seeds until fragrant, about 5 minutes. Add to fennel mixture. In a medium bowl, toss tomatoes with balsamic vinegar, 2 tablespoons olive oil, red onion, basil, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Set aside.
Using a teaspoon, remove the chokes of the trimmed artichokes. Rub the hearts with the lemon. Transfer to a medium bowl. Juice lemon halves over artichokes, and add water to cover. Using a very sharp knife or Japanese mandoline, slice artichoke hearts to a 1/8-inch thickness.
In a large saute pan, heat 2 tablespoons olive oil over high heat. Add artichokes, and saute, stirring constantly until just tender, about 5 minutes. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Add cilantro, and stir to combine. Set aside.
In a medium saute pan, heat remaining teaspoon olive oil over high heat. Add shrimp; season with remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Saute until pink and firm, 3 to 5 minutes. Remove from heat.
Transfer marinated fennel to serving dish. Place artichokes on fennel. Add tomato salad to center. Top with shrimp, and garnish with olives.