Preheat oven to 425°F. Scrub beets with a vegetable brush. Wrap each beet separately in foil, making sure the beet is completely wrapped in foil. Set beets in a small baking pan. Bake for 50 to 60 minutes or until beets are almost tender (pull back the foil and insert a small sharp knife into the beet – you should be able to insert the knife into the center of the beet easily but with a little resistance). Set beets on a wire rack to cool (still wrapped in the foil).
Meanwhile, in a small bowl combine onion, vinegar, and 1/8 teaspoon salt. Press down on onions to get them as covered with vinegar as possible. Cover; let stand at room temperature for 1 hour or chill up to 3 days.
In a small saucepan combine quinoa, water, and 1/8 teaspoon salt. Bring to boiling; reduce heat to low. Cook, covered, over for 15 minutes or until water is completely absorbed. Remove from the heat. Set aside to cool completely.
When beets are cool enough to handle, use a vegetable peeler to peel off the skin. (Note: do this over the sink and use a slow flow of water to help rinse off the skin as you peel them. Also, to avoid staining your hands, wear clean plastic gloves.)
Trim off the bottom and a small slice from the top of each beet; discard. Cut beets crosswise into four slices (about ½-inch thick each). Lay slices flat on the cutting board. Use a 2- to 2 ½-inch heart shaped cookie cutter to cut a heart from each beet slice. Arrange beet hearts in a single layer on one side of a foil-lined half-sheet pan (18x13x1-inch size). Save scraps from beet slices for another use**. Set pan with beets aside.
Peel sweet potato. Cut potato crosswise in half; cut each half the long way into ½-inch thick slices. Cut those slices the long way into ½-inch thick strips. You will end up with pieces that look like large French fries. Arrange sweet potato strips in a single layer on the other half of the sheet pan with beets. Drizzle beets and potatoes with 2 tablespoons oil. Sprinkle with ¼ teaspoon salt. Toss potatoes to fully coat with the oil; arrange back to the single layer. Turn beets so they are coated with the oil.
Roast beets and potatoes in the 425°F oven for 25 to 30 minutes or until beets are completely tender and potatoes are just tender and starting to brown, stirring potatoes once halfway through roasting (no need to turn beets).
Drain onions, reserving the drained vinegar. Set onions aside. In a large bowl toss together cooled quinoa, arugula, and lettuce. Set aside.
For the Dressing, in a small screw-top jar*** combine ¼ cup oil, the orange juice, mustard, 1 tablespoon of the vinegar drained off the onions, and ¼ teaspoon salt. Cover; shake well. Add ¼ cup of the dressing to the quinoa mixture; toss gently to coat.
To serve, arrange quinoa mixture on a serving platter. Top with roasted beets and potatoes. Top with drained onion. If desired, sprinkle with fresh pepper. Serve with remaining dressing.