My iPod Touch 4 is under warranty, but yesterday, someone broke the screen. It still works, but is very scratched up and has decreased touch response. Will Apple repair it for free, will I have to pay, or will they refuse to fix it at all?
Yes, they will replace a broken screen for an out-of-warranty replacement price. You might get lucky if you kindly ask if they'll do a one time exception to replace your device.