To prepare the vinaigrette: Whisk vinegar, water, mustard, caraway seeds, salt and pepper together in bowl. Whisking constantly, slowly drizzle in oil until emulsified. (Vinaigrette can be refrigerated for up to 2 days; whisk to recombine before using.)
For the salad: Adjust oven rack to middle position and heat oven to 400 degrees. Toss potatoes, oil and salt together in bowl, then spread in even layer on rimmed baking sheet lined with aluminum foil. Roast until potatoes are beginning to brown, 15 to 20 minutes, flipping slices halfway through roasting. Let potatoes cool for 5 minutes, then season with salt and pepper to taste. (Sweet potatoes can be refrigerated for up to 2 days.)
Toss kale with half of vinaigrette in large bowl to coat, then season with salt and pepper to taste. Transfer to serving platter and top with rice, sweet potatoes, apple, feta and cranberries. Drizzle with remaining vinaigrette and serve.