Set salmon on a cooling rack in a rimmed pan, sprinkle fillets all over with sea salt, and chill uncovered at least 2 hours and as long as 5 hours.
Heat grill to medium-high (about 450°). Fold a 12- by 20-in. sheet of heavy-duty foil in half crosswise. With a knife tip, poke dime-size holes through foil about 2 in. apart. Oil one side of foil. Rub fish all over with oil.
Set foil with oiled side up on cooking grate. Set fillets slightly separated, skin side down, on foil. Grill, covered, until fish is barely cooked through, 7 to 12 minutes. With a wide spatula, slide fish from skin to a platter and tent with foil. Cook skin on foil until crisp, 2 to 3 more minutes. Remove foil from grill, then gently peel off skin, using fingers or a wide spatula (skin may break into pieces).
Serve salmon immediately with crispy skin, rice, nori, lemon, and furikake.
*A salty-sweet shake-on condiment, sold at Asian foods stores and at asianfoodgrocer.com.
Note: Nutritional analysis is per serving.