Place all ingredients in a blender, then process until very smooth. Strain through a sieve, then set aside until ready to serve.
Add enough neutral oil to come up about 3-inches in a large saucepan or pot. Heat over medium-high heat.
Whisk together rice flour and soda water until very smooth.
Add the calamari and watercress, then thoroughly coat. Carefully shake off any excess batter, then transfer the calamari and the watercress to the hot oil. Cook in batches until the calamari and watercress are a light golden brown. Use a spider to transfer to a paper towel.
Place fried calamari and watercress in a large mixing bowl. Add minced shallots, chives, chopped mint, then drizzle with as much of the chili-lime dressing as you like. Toss well, then serve with thinly sliced lime wedges, Thai chilis, mint, and crushed peanuts.