The game was scored incorrectly. All of the white stones have been erroneously marked as dead (and hence counted as territory and captures for black), while in fact they should all be considered alive.
Also, the game was not quite over, since both players should want to play F1 in order to maximize their points (however, this would not have made a big enough of a difference to change what should have been the outcome, a white win). C4 is also an unresolved ko, and J3 is in atari (should eventually be either captured or connected to living stones).
If black doesn’t do it, white could play C4 to capture the black stone in D4. Now it’s black turn and the white stone in C4 would be atari, but black cannot re-capture it immediately due to the Ko rule. So black has to play elsewhere, and white can now play in D4 to connect its stones.
Yes. The point is that this ko is an opportunity for white to get +1 point (by capturing black stone, and then resolving the ko). So this opportunity should either be denied by black, or taken by white, but leaving it unresolved means there is still a point to be made on the board.