Boat safety ground connected to battery charger chasis / frame

In the North American marine / Boat systems:

All battery chargers (This case Centaur 24/60) have a stud on the chasis that MUST be connected with a green/yellow wire to the safety ground network/circuit on the boat.

  1. correct?

  2. Shall that chasis be connected with another wire to the output negative terminal of the battery charger? Why?

  3. And to the input AC safety ground ?

  4. How to size the gauge of those wires?

  5. Are above mentioned connections, already made as internal connections from manufacturing?