In a bowl, combine almonds, raisins, capers, almond oil, and lemon juice; set aside.
Heat 2 tablespoons oil in a large skillet over medium high heat; add mushrooms and cook until browned, but tender, about 8 minutes, stirring occasionally.
Add green onions, season with salt and pepper, and cook until lightly browned, 3 minutes (keep warm).
Meanwhile, sprinkle fish lightly with salt and let stand 5 minutes; rinse off salt and pat fish dry with paper towels.
Heat 2 more tablespoons of olive oil in a skillet, over high heat, and cook fish (in batches if necessary, adding more oil as needed), until browned on the bottom; turn fish and cook until opaque, about 2 minutes longer.
Serve the fish topped with the caper-almond dressing and the mushrooms and green onions along side.