Is there a reason you're not just baking a standard thickness and splitting it into layers? This is going to give you more control.
If you have troubles moving the layers without breaking them, have a piece of cardboard handy (traditionally a cardboard cake round would be used by any would work) and after cutting the cake horizontally, lift up the edge of the top piece to slide the cardboard under and then proceed to push it all the way under the top layer before carefully removing the layer. Proceed with the next layer.
If they cake is a bit dry but not crunchy, moisten the cut surface by brushing with simple syrup on its own if you don't want any added flavor, or add a bit of a complementary-flavored liqueur to the syrup before moistening.
Delicious variations abound, so it is hard to make absolute statements of what is "officially" a ladyfinger. In my pastry class, we were taught that the classic recipe for ladyfingers is close, but not identical, to genoise. Store-bought ladyfingers can be anything from, essentially, a meringue to a shortbread cookie.
Foam-based batters -- i.e., those that do not use chemical leveners or yeast -- can be divided into two categories: whole-egg and separated-egg. The main difference in results is that the latter tend to be stiffer and can better tolerate being overcooked a little. The primary example of whole-egg batter is the genoise cake. Because the whites are whipped together with the yolks (and sometimes extra yolks are added), it is a finicky batter, requiring more skill to assemble properly than others, but when it works, it is more tender. Separated-egg batters are far more common, as they are easier to assemble; the key is that you whip the whites into medium-to-stiff peaks, then fold it back into the rest of the batter. Examples include chiffon, dacquoise, and the French "biscuit" cakes.
Most recipes for ladyfingers use a separated-egg batter; others use a simple meringue. The meringue version will make a crisp cookie, the version with with the yolk, soft. Either will work well for uses like tiramisu or trifle.
Here is a recipe for ladyfingers from Allrecipes.com and a recipe for genoise from Epicurious. For my ladyfingers, I add a pinch of salt and some flavorings, such as vanilla or nut extract, but the base recipe is essentially the same.
Best Answer
Yes, they can be used for other dishes. I've never done it myself, so I cannot elaborate.
I scanned the Amazon reviews for a panettone paper. I saw people had used them for sweet bread, muffins, some used it for cheesecake. I imagine the papers could be used for souffles and quiches.
One Amazon reviewer mentioned you may need to increase the moisture in your recipe since the paper soaks up some of the liquid.
In any use, I would pan it in a way where spillage would be contained.