Whisk together all of the ingredients in a small bowl. Cover and chill.
To make the jalepeño-shikuwasa jam paste
Place the lemon zest, flesh and jalepeno into a small processor. Process until smooth, then pass through a fine-mesh sieve. Transfer the contents left in the sieve into a small bowl, then add in the shikuwasa jam and salt. (You can toss or reserve the leftover liquid in another application if you like.) Cover and chill.
To make the beignets
Place the seaweed into a bowl and cover with plenty of warm water to soften for about 10 minutes. The seaweed will expand considerably during the time. Drain the water off the seaweed and refill the bowl again with enough warm water to cover the seaweed and soak again while you make your beignet batter.
Place the 00 or AP and rice flour, baking soda and salt into a large bowl. In a separate bowl, whisk the Ener-G and water together. Add in the silken tofu and carbonated water (start with 3/4 cup) and whisk until smooth, then add it to the flour mixture, combining it together gently until well-blended. Add a bit more carbonated water as needed to achieve a pancake batter-like consistency. Do not overmix.
Drain the seaweed and give it a squeeze with your hands to remove some of the excess water. Roughly chop, then fold into the batter.
Place several inches of canola into a small saucepan. Heat over medium-high heat for several minutes. You can either use a deep-fry thermometer to confirm a 350-degree temperature or just insert a wooden spoon into the bottom of the pan. If bubbles form around the wooden spoon immediately, you are ready to fry.
Drop tablespoon-sized amounts of batter into the hot oil (only 3 or 4 at a time), and fry for about 4 minutes or until deeply golden brown, flipping them around to ensure even frying. Transfer to paper towels to drain. If your oil gets too hot, just lower the temperature slightly in between batches to prevent burning.
Serve the beignets immediately with the chilled lime mayo and sweet and spicy jam paste.
The leftover oil can be completely cooled, strained and stored in the refrigerator and used a couple more times before discarding it.
I used the leftover batter the next day to make savory pancakes—I just added a bit of baking soda to the batter, then poured 2 TB-sized portions into a hot oiled skillet, frying for a few minutes on each side over medium high heat.