1. Set aside 8 apricot halves. In a 1- to 2-quart pan, bring remaining apricots and 1/2 cup water to a boil, then cover and simmer just until fruit is plumped, about 10 minutes.
2. Meanwhile, combine crumbs and melted butter. Pat evenly over bottom and 3/4 inch up side of an 8-inch cheesecake pan with removable rim.
3. In a food processor, smoothly purée cooked apricots and any liquid. Add liqueur, cream cheese, 3/4 cup sugar, egg, and egg whites. Whirl until smooth (or combine ingredients in a bowl and beat with a mixer until smooth).
4. Scrape mixture into prepared pan. Bake in a 350° oven until cake jiggles only slightly in the center when gently shaken, about 25 minutes.
5. Mix yogurt cheese with remaining 1 tablespoon sugar. Spoon onto cake and gently spread to cover top. Bake just until topping is heated, about 5 minutes.
6. Run a thin-bladed knife between cake and pan rim. Refrigerate cake, uncovered, until cool, about 2 hours. Remove pan rim.
7. Melt jam (in a microwave oven or in a small pan over medium heat), stirring often. Rub jam through a fine strainer into a bowl; discard residue. Spoon about 3/4 of the jam evenly over cold cheesecake, then spread gently to coat evenly.
8. Cut each reserved dried apricot half in half and arrange pieces on cake. Spoon remaining jam onto apricot pieces to coat evenly. Chill until jam is set, about 10 minutes. Serve, or if making ahead, cover with a bowl or a foil tent and chill up to 2 days. Cut cake into wedges.