Special equipment: a deep-frying thermometer
For the sweet orange sauce: Combine the orange juice and honey in a medium saucepan and bring to a boil over medium-high heat. Reduce the heat slightly and cook at a very brisk simmer until the mixture is syrupy and reduced to a little less than 1/2 cup, 15 to 20 minutes. Remove from the heat. Let cool slightly, then whisk in the oil, lemon juice, parsley and crushed red pepper. Transfer to a ramekin or small bowl.
For the fried calamari: Fill a large, wide pot with 1 1/2 inches oil and heat over medium-high heat until it registers 350 degrees F on a deep-frying thermometer. Line a tray with paper towels. Meanwhile, whisk together the flour, cornstarch, paprika, 2 teaspoons salt and 1 teaspoon pepper in a wide, shallow bowl.
Toss the squid and chiles with the flour mixture, making sure all the squid rings are separated and everything is thoroughly coated. Transfer about a third of the squid and chile mixture to a kitchen spider or slotted spoon and shake to remove the excess flour. Carefully add the squid and chiles to the hot oil and fry until crisp and just barely golden, 1 to 1 1/2 minutes. Transfer to the prepared tray with a slotted spoon and sprinkle generously with salt. Repeat the sifting and frying process with the remaining squid, making sure to return the oil to 350 degrees F between batches.
Transfer to the fried squid to a plate and sprinkle with the parsley. Serve with the lemon and orange wedges and the sweet orange sauce for dipping.