To prepare granita, place blueberries in a food processor or blender; process until smooth. With food processor still on, slowly pour 1 cup water through food chute; process until well blended. Strain blueberry mixture through a fine sieve into a bowl; discard solids.
Combine 1/2 cup water and 3/4 cup sugar in a small saucepan over high heat, stirring until sugar dissolves. Stir sugar mixture and 3 tablespoons juice into blueberry mixture. Pour mixture into a 13 x 9-inch glass baking dish; let cool to room temperature. Freeze 1 1/2 to 2 hours or until ice crystals begin to form. Remove mixture from freezer; stir well with a fork. Return dish to freezer; freeze 2 hours, stirring every 30 minutes or until slushy. Cover and freeze 1 hour.
To prepare compote, place 1 cup strawberries in a food processor or blender; process until smooth. Strain strawberry mixture through a fine sieve into a bowl; discard solids.
Combine 1/2 cup water, 1/3 cup sugar, and rind in a medium saucepan over medium-high heat; bring to a boil. Cook 1 minute; remove from heat. Discard rind. Add puréed strawberries, quartered strawberries, blueberries, and 1 teaspoon juice to pan; stir gently to combine. Let cool to room temperature. Cover and chill. Spoon compote into each of 8 bowls; top with granita.