If you lose the original, the photocopy can speed up the process of obtaining a replacement. It won't hurt to take your driver's license with you, but it is your passport that is considered valid identification at the border, in the banks, at the airport, etc. If you plan on staying in Germany for more than three months, you do need a visa to leagally reside there. Crime rates are relatively low compared to the US, especially violent crimes. However, don't become overconfident.
Pickpockets abound in Europe, and petty theft can occur any time.
Common sense is the rule when dealing with your own safety. Keep the flaps on your bags closed and toward you. Carry your cash close to your body. And if you encounter strange or frightening people, simply avoid them. Germans, for the most part, keep to themselves, but they are very helpful to people in need.