Let salmon come to room temperature, about 1 hour. Meanwhile, on a plate, toss onions with 1 tbsp. oil and 1/4 tsp. each salt and pepper; set aside. In a bowl, mix yogurt, dill, and chives; chill.
Set salmon skin side up. With a small, sharp knife, score thickest part of fillet crosswise through skin only in 3 or 4 places, making cuts 3 in. long. Brush skin with 1 tbsp. oil. Combine 1 tsp. salt and 1/2 tsp. pepper; sprinkle all over fish. Combine remaining 2 tbsp. oil and the sumac; brush over salmon flesh but not skin. Set aside.
For charcoal, ignite a full chimney of hardwood charcoal on firegrate of a charcoal grill. Spread in an even layer and set cooking grate in place. For gas, heat a gas grill to medium (350° to 400°).
Grill onions, covered and turning once, until lightly charred, 2 to 3 minutes total. Transfer to a board. For charcoal, if needed, let grill cool, uncovered, to medium (350° to 400°).
Clean cooking grate with a grill brush. Oil grate, using tongs and a wad of oiled paper towels. Set salmon skin side down on grate. Grill, covered, until thinner parts of fish feel firm to touch and only the top 1/2 in. still looks raw (cut to test), 8 to 10 minutes.
With 2 wide metal spatulas, loosen fish from skin. Slide a spatula and a rimless baking sheet under fish, leaving skin on grill, and transfer to a cutting board; tent fish with foil and let rest at least 10 minutes. The carryover heat will continue to cook it.
Slide a spatula under salmon skin to loosen; if it isn't completely brown, turn it over and cook, covered, a minute or two. Transfer to a cutting board and coarsely chop; put cracklings in a bowl.
Cut 1 green onion into 1-in. pieces, then into thin strips. Finely chop remaining onions, stir into yogurt, and season with more salt and pepper to taste. Top yogurt with onion strips. Serve salmon with yogurt and salmon-skin cracklings.
*Find sumac, a ground dried berry, in the spice aisle and at worldspice.com.