Preheat oven to 350 degrees with rack placed in lower third. Line bottom of a 10-inch diameter tube or angel-food cake pan with parchment; set aside. Sift together flour, 1/2 cup sugar, and salt onto a sheet of waxed paper. Resift into a medium bowl.
In electric mixer fitted with whisk attachment, beat egg whites on medium-low speed until foamy, about 1 minute. Beat in cream of tartar and vanilla. Increase mixer speed to medium-high; beat until whites are nearly stiff, about 2 minutes. Reduce speed to medium-low, and then beat in remaining cup of sugar, two tablespoons at a time, until peaks are stiff but not dry.
Sift reserved flour mixture over egg-white mixture. Using a rubber spatula, gently fold mixture until all the flour is incorporated. Transfer batter to the prepared pan. Run a knife through the batter, touching the bottom of the pan, to eliminate air pockets. Smooth the top with a spatula.
Bake until top of cake is golden and the cake springs back when pressed lightly, 35 to 40 minutes. (If top begins to darken, tent with foil.) Invert pan onto its legs or hang it over the neck of a bottle or funnel; let cake stand upside down in the pan until completely cool, about 1 hour. Run a knife around the sides of the cake; remove cake onto large cake plate or cake stand, widest end down; set aside. Repeat recipe to make a second angel food cake.
While second cake is baking, use crab-shaped cutter to cut 20 crabs from jelly candies. Set aside. Remove cooled second cake from pan; trim arched golden side so it is level. Place on top of first cake, trimmed side down. To shape the bucket, place 6-inch plate on top of cake for a cutting guide. Starting at edge of plate, use a serrated knife to cut a straight line down at a diagonal to bottom of 10-inch base. (Bottom layer gets trimmed very little.) Work around cake until sides are even. Reserve the trimmings to use for the starfish cutout that sits on top of the cake.
In an electric mixer fitted with the paddle attachment, beat cream cheese and butter until soft. Sift in sugar; add vanilla. Beat on medium-high speed until light and fluffy. Frosting may be made up to 1 day ahead. Rebeat frosting before using.
Using a clean, dry brush, brush crumbs from trimmed cake. Remove top layer; set aside. Using an offset spatula, frost top of bottom layer with 3 tablespoons frosting. Replace top cake. Frost entire cake with a thin layer to seal. Refrigerate until crumb coat of frosting is firm, about 20 minutes. Frost cake with a thicker layer, saving 2 tablespoons for starfish for top of cake.
Tilt cake; dust side with cookie crumbs. Apply candy crabs around sides. From reserved cake trimmings, use 3 1/2-inch star cutter to cut out starfish. Frost with reserved frosting; dust with sprinkles, then cookie crumbs. Place on top of the cake.
To serve cake, cut through one layer at a time, cutting halfway down.