External 5V Power and USB Serial

Having used counterless Arduinos and clones, I can tell you that you can connect both without worrying about any danger. Unless you have a very faulty board, your pc won't be damaged, almost surely neither will the board, as is should select the most powerful source, between your usb or a battery/external PS, while leaving untouched the serial line.

If you are new to something, you should start with reading manual.

Here's what official Wiki page of arduino nano says: https://www.arduino.cc/en/Main/ArduinoBoardNano

Power:

The Arduino Nano can be powered via the Mini-B USB connection, 6-20V unregulated external power supply (pin 30), or 5V regulated external power supply (pin 27). The power source is automatically selected to the highest voltage source.