Marinate squid rings in buttermilk, refrigerated, for 2 to 6 hours. In blender or food processor, puree almonds, arugula, garlic and paprika into coarse paste. Slowly add half the olive oil while processing. Scrape down sides of bowl. Slowly add remaining olive oil and the lemon juice. Scrape pesto into bowl; mix in crumbled feta. Season to taste with salt and pepper. Set aside.
Pat squid rings dry on paper towels. Dip rings in flour, then egg, coating thoroughly, and then in breadcrumbs. Heat vegetable oil in large saucepan to 375° F. Gently place breaded squid rings in oil; fry until golden brown, 1 to 1-1/2 minutes. Do not overcook or squid will become tough. Remove from oil and drain on paper towels.
Squeeze a little lemon juice over squid; season with salt and pepper. Serve with pesto on the side.