Rice Puddings with Caramel Gala Apples

Bring 3 cups water and 1/4 teaspoon salt to boil in heavy large saucepan. Add rice and boil 10 minutes. Drain rice; discard cooking water. Rinse saucepan. Combine milk and sugar in same saucepan; bring to boil over medium-high heat, stirring until sugar dissolves. Add rice; reduce heat to medium and simmer until rice is very tender, most of milk is absorbed, and pudding is thickened but still creamy and reduced to scant 3 cups, stirring occasionally, about 35 minutes. Remove from heat. Stir in vanilla extract. Transfer rice pudding to medium bowl. Press plastic wrap onto surface of pudding; let pudding cool to room temperature. Refrigerate until cold. DO AHEAD: Can be made 2 days ahead. Keep refrigerated.
Peel apples; quarter through stem end and remove core. Cut each apple quarter into 4 slices, then cut slices crosswise into thirds. Combine sugar and lemon juice in medium nonstick skillet. Stir over medium-high heat until sugar dissolves and syrup is medium amber color, occasionally swirling skillet, 3 to 4 minutes. Remove from heat; add butter to skillet and swirl until melted (mixture may bubble vigorously). Return skillet to medium heat; add cider and pinch of salt and bring to boil. Add apples and simmer until tender, stirring often, about 6 minutes. Add 1/2 cup whipping cream and boil until sauce thickens slightly, about 2 minutes. Transfer apples with caramel sauce to heatproof bowl. Cool caramel apples until lukewarm or room temperature. DO AHEAD: Caramel apples can be made 1 day ahead. Cover and refrigerate. Stir over medium heat until just warm before using.
Divide half of caramel apples among 6 Martini glasses or lowball glasses. Top each with rice pudding, dividing equally. Top with remaining caramel apples, dividing equally. Garnish each with dollop of whipped cream, if desired, and serve.