Can someone copy biometric data such as a fingerprint?

Biometrics are a representation of a person and are useful for authentication purposes only if they can be acquired repeatidly for comparison with a reference template. So, yes most if not all useful biometrics can be copied and potentially played back. Voice can be recorded, fingerprint can be acquired from the traces left on a reader.

Recent biometrics systems however can check if there is a live finger on the sensor or reject a verification if the acquired biometrics is too close from either the verification template or the previous image used.

The reference template used in biometrics systems should also be secured either using a smart card or by encrypting the database that holds them.