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As to your first question greased parchment paper has worked for me. As to your second question, if you want to make it look presentable, try a adding a bit of acid to your caramel to stop the sugar from crystallizing, ie bit of lemon juice or cream of tartar, that way it will set up properly atop your pastry.
Make the cake layers and filling, then fill and stack the cake. Make the caramel and pour/spread it onto buttered parchment on a baking sheet. Let it cool. When it's firm but not hard, use a lightly oiled pizza cutter or knife to cut it into eight, 10 or 12 wedges, depending on how big you want each serving to be. Let the caramel cool completely. Just before serving, lay the caramel wedges at an angle on the cake--it should look sort of like a pinwheel. Slice between the wedges and serve.
maybe creating a collar a couple of inches taller than the cake to go all the way around it will create a dam so the caramel has a chance to set. could it also be possible that the caramel is too warm when you pour it? caramel is fairly straightforward, but it can also be challenging, and since you mention that you are having extreme results (too runny or too hard), maybe you just haven't hit upon the magic balance of this particular recipe?