No, because the green arrow allows me to proceed but I must give way to the approaching vehicle: Correct
The green arrow indicates that you have the right to proceed in the direction of the arrow (in this case, to turn right). However, it does not necessarily give you the right of way over other road users. If there is an approaching vehicle or pedestrians, you are still required to give way to them, even if the green arrow is lit.
Yes, because the green arrow means I must turn: It is incorrect because the green arrow allows you to proceed in the direction indicated, but it doesn’t give you absolute right of way. You must still be aware of other road users, and you may need to yield to them if necessary.
No, because the red light means I cannot turn: It is incorrect because the red light would prevent you from proceeding, but the presence of a green arrow usually overrides a red light for a specific turn.