Baking – Is it bad if a sponge cake sits out for a couple hours before cooking

A couple things:

• Unless the recipe (or experience) says otherwise, place items in the middle. Putting something higher in a conventional (non-convection) oven should make the top cook quicker than the bottom. This may account for the top drying out when the rest isn't done yet.
• As @ElendilTheTall says, check your oven temperature. Your oven is probably running much lower than it should be. On most ovens, you can adjust the dial so its right.
• Make sure you're using the same size (and material) pan as the recipe. Thicker cakes take longer to cook, and some pan materials are slower than others.

I looked up several recipes, and all gave times under 30 minutes.

If you use a sandwich bag with a corner cut out of it, you now have a make-shift piping bag :). Just fill the bag, twist it, and then cut a corner out.

The problem I see with trying to bake a cupcake with a custard center, is this:

Even if you have the custard pre-made (and probably chilled) It won't be hard enough to "wrap" in the cupcake batter. Typically cupcake batter is not very firm, and you'd end up with a mess. This may work with a heavier dough, perhaps a pastry dough or something. The custard will definitely hold up just fine, it's just the act of somehow suspending it in the cupcake batter long enough for the batter to set into cake, that is slightly impractical.

The only other thing I could think of is perhaps making a gelatin custard and hope that it will hold up long enough for the batter to cook. The downside to this, obviously, is that you'll end up jello custard if the cupcakes aren't eaten warm, and on top of that, trying to hit the perfect gelatin amount would be VERY hard.

Freezing the custard will likely not work.