Can I use an iPhone 5 screen protector on the new iPod touch 5?

Both screens are the same size however on the iPhone it's got a hole at the top for the earpiece, so it might not protect the front facing camera on the iTouch or it might just go over it completely, blocking the camera.

It depends if the size is the same

The size wouldn't matter as both have a 4.0 inch screen but if it's a clear screen protector it'll be fine.

No, because the iPhone has an extra hole near the top of the screen for the mic. And also the cameras are at different positions, so there would be lots of extra space and it would cover the camera.