In a food processor, grind the cookies and sugar into crumbs. Stir in melted butter. Press the mixture into the bottom of a 9-by-13-inch pan to form a crust and chill while preparing the filling.
In a food processor, combine the ricotta and cream cheese until smooth, then add the powdered sugar, lemon juice, and rind, and combine until no lumps remain. Transfer to a bowl and fold in the whipped cream. Spoon half the filling over the crust and spread it evenly to the edges, then add a third of the berries. Spoon remaining filling over the berries and spread it evenly, to the edges. Chill at least 4 hours.
When ready to serve, mix the remaining berries with jam to glaze them. Spoon them over the cheesecake, keeping away from the edge. Sprinkle kiwi pieces and mint leaves. Serve chilled with a large spoon.
