Crown Molding LED Light Wiring
Ideally you would inject power every 2.5 m or 5 m. This is to bypass the FPC strips' high resistance. Which is also why ideally you would run dedicated wires. But having a thick wire run in parallel does work as well. Which leads to your 3rd question, the gauge required depends on the current you are carrying, the voltage that is being used and the acceptable voltage drop. The smaller the gauge the thicker the wire and the less resistance you have to worry about. Google for a voltage drop calculator.