How to check which data gets cached by App?

What an app stores on your phone is impossible to say without going through the source codes or at least examining the app's data folder.

That being said, valuable information related to banking (balance, account ID, your personal information, log in information etc.) are stored in the servers of the bank since it is actually them who own those information. The app merely accesses them.

As for the log in part, banking apps use a method called hashing. I won't annoy you with all the details but long in short, the reason they can't give you your old password or PIN code when you forget it is that, they don't store it as well. They store its hash. They check the hash of your password to see if it matches the one in their database and you can't reverse engineer a hash to find the password. Therefore as long as you don't choose to stay logged in, no harm can come.

But if you want to delete all personal datas related to any specific app (user data or cache) you can do it like here

Or, you can tell your bank to block every action other than viewing account information on mobile banking application.