Is the cornstarch critical (or can I just put some more flour instead)? How exactly does it act as a different thickener (from flour) in the bakin...

To the second part of your question, cornstarch thickens quickly with relatively less cooking than flour. If you cook cornstarch too long, it will break down as a thickener. Makes sense for food that you want to thicken which doesn't need to be cooked too long. Flour, on the other hand, needs to be cooked longer (most of the time, require boiling) in order to thicken and cook out the raw flavor. And you will need a lot more flour to thicken in comparison to cornstarch.

The cornstarch is in the crust, not the filling. So it's not used as a thickener. I think it's there to make for a lighter, more tender crust. I think you can get away with using all flour. There's a bit of cornstarch in the confectioners sugar already. Or maybe you can substitute with a cake flour or pastry flour which has less protein.