Since I found many beginners struggling with understanding why the 2 eyes are needed, I'd like to point out why a group with 2 eyes is alive.
The "a group needs 2 eyes in order to live" is actually not a rule, it is only a consequence to another rule you've learned. Remember the rule that are not allowed to do suicide moves. Why is that?
A stone with no other stone around has 4 liberties.
If the last liberty is gone, a stone or a group of stones are captured and will be removed from the board (directly).
Now black can't play at the marked position because it would be considered suicide. The black stone wouldn't have any liberties and no group / stone with no liberties can exist on the board. So it would have to be removed right the moment it was played.
But now consider this shape of connected stones:
In this situation, the group can be captured.
This is because the stones have only 1 last liberty left (this is called 'atari', by the way). The moment black plays the stone, the other group is captured and the played stone directly gains liberties; that's why it is not a suicide move.
Note: The group that was just captured had only 1 eye.
In this situation the group has 2 liberties. If black would be able to steal those 2 liberties away with 2 allowed moves, the group would die. In this situation however, black can't play at 1 or 2, because it wouldn't have any liberties left. This would be a suicide move. The white group on the other hand still has 2 liberties.
Note: This group has 2 eyes.
Given that rules, I think you should be able to tell now, which group is alive and which isn't. The game ends when both players pass or one side gives up. Dead stones become points for the group that captured it.
The more you advance in Go the more you'll be able to judge whether a group is alive or not and if it makes sense to play a stone in an already defined territory or not.
In your scenario 1, both white groups only have 1 eye. If white passes and black passes, the game will end. All white stones will be removed, (without Komi) white has 0 points, black has 71 (all blank points + all dead stones).
In your scenario 2, one white group has 2 eyes and cannot be killed by black, the other one has one eye. If both player pass, the game will end. The dead white stones in the lower left corner will be removed. (Without Komi) white has 4 points, black has 50 points.
But as already mentioned, normally the game wouldn't be considered finished yet.
