Put the rice, water, and a pinch of the salt in a medium saucepan and bring it to a boil. Reduce the heat to low, cover, and let the rice simmer until the water is absorbed and the rice is tender and fluffy (about 30 minutes). Let the cooked rice cool for 15 minutes.
While the rice is cooking, place the shredded zucchini in a colander over the sink. Sprinkle a pinch of salt over it and toss well. Let the zucchini sit for about 15 minutes, or until it gives up some liquid. Squeeze out any excess liquid.
In a large mixing bowl, combine the rice, shredded carrots, drained zucchini, minced parsley, and minced scallions. Add the garlic powder, cumin, coriander, and remainind 1/4 teaspoon of salt (or to taste).
In a separate bowl, combine the eggs and rice flour. Mix well until smooth. Add this to the vegetable mixture and mix well.
Heat a nonstick frying pan over medium-high heat, and add 2 tablespoons of olive oil. Form the vegetable batter into patties about 3-inches in diameter. When the oil is hot, add 3 or 4 to the pan (however many fit comfortably in your pan) and let them cook for about 4 minutes on each side. Keep an eye on the heat, you may need to turn it down a bit so the fritters cook evenly and don't burn. Repeat with the remaning batter.
To make the yogurt sauce, combine the Greek yogurt, parsley, lime zest and juice, and a pinch of sauce in a small bowl.
Serve 2 fritters with about 1/4 cup of the yogurt sauce for each portion.