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