If I'm out of the US traveling and someone calls me and I don't answer the call will I be charged? If that person leaves a voicemail and I don't call to check my voicemail would I be charged?

If you don’t answer (as opposed to rejecting the call) you no deberían be charged. If you call to check your voicemail, you will be charged for the call. This is why you should check your messages via the Visual Voicemail app. Here are some international roaming hints.