1. Combine apple and lime juice in a bowl; toss. Add onion, chilli, 1 tablespoon cilantro, and 1/8 teaspoon salt; toss. Cover and chill.
2. Combine squash, sweet potato, and onion in a colander; drain 30 minutes, pressing occasionally with the back of a spoon until barely moist.
3. Combine potato mixture, remaining 4 tablespoons cilantro, remaining 1/2 teaspoon salt, flour, and next 5 ingredients (through egg) in a large bowl; toss well.
4. Heat a large skillet over medium-high heat. Add 4 teaspoons oil to pan; swirl to coat. Spoon 1/4 cup sweet potato mixture loosely into a dry measuring cup. Pour mixture into pan; flatten slightly.
5. Repeat procedure 4 times to form 5 latkes. Saute 3 1/2 minutes on each side or until golden brown and thoroughly cooked. Remove latkes from pan; keep warm.
6. Repeat procedure twice with remaining oil and sweet potato mixture to yield 14 latkes total. Serve with salsa and a greens of your choice.