Blend jalapeno, red pepper, garlic, sugar, fish sauce, salt, and 3 Tbsp. oil in a blender until smooth. Transfer marinade to a bowl and add shrimp and calamari; toss to coat. Let sit 10 minutes.
Heat remaining 1 tablespoon oil in a large nonstick skillet over medium-high/high. Make sure oil is very hot before adding the seafood. (Oil should almost be smoking.) This is important for achieving crispy edges on the shrimp and calamari. Working in batches if needed, add shrimp and calamari, leaving marinade behind, and cook, turning once, until lightly caramelized and browned around the edges, about 2-3 minutes per side. (Actual cooking time depends on the size of the shrimp. If using smaller shrimp, cooking time will be less.)
Remove shrimp and calamari from the pan and place on a platter.
Turn down heat and add basil. Cook until basil is wilted, less than 1 minute.
Using tongs, add wilted basil to the shrimp and calamari. Then use a spatula to scrape up as much of the caramelized brown-bit goodness remaining in the pan and add to the dish. Serve with lime wedges and rice, if desired.