Put quinoa, water, and 3/4 teaspoons salt into a saucepan and set over high heat. Bring to a boil, then cover, reduce heat to low, and simmer until all the water is absorbed, about 20 minutes.
Meanwhile, in a small bowl, whisk together the lemon juice, vinegar, honey, and remaining 1/4 teaspoon salt. Add the shallot and stir. Let sit 10 minutes, then whisk in the olive oil.
When the quinoa has absorbed all the water, uncover the pot and continue stirring the grains over the heat until they are dry and fluffy. Transfer to a serving bowl and toss to cool and fluff the quinoa. Add the mango, avocado, and scallions and toss together. Pour the dressing over the salad and toss again. Sprinkle with feta cheese and serve.