1st example: yes blue can take the yellow king, game over. (could also take the yellow Q of course)
> How does red stop this?
red moved before blue. he was in check (and couldn't take blue king) so he has to move out of check. no way to stop it.
2nd example: blue eats yellow king of course. this is just the prime example: red moving the N is just a terrible move! by all means of chess logic, such a move has to be fatal. in 2pc the N would be pinned. Allowing the N to "unpin" should change nothing, the king shall be captured next move. The yellow king gets captured first. No matter how you twist it, the logic is the same: even if allowed unpinning in 2pc, to give a check or even a checkmate, the opponent will just take your king, he gets there first, he wins, it's too late, nothing else matters.
Here we do see slight shift in strategy: to play for a king capture is stronger that to play for a checkmate. This to me is justified though. A king capture is just better/more direct than a checkmate. A checkmate implies a king capture will follow, but it will always be one move slower than actually taking the king.





this bishop is not pinned:
..regardless if it's a red or a yellow king.
As soon as blue plays Bm9, the alarm bells have to go off for Yellow. It is the strongest possible, most direct threat that exists in the game. Still looks very natural to me that Yellow has to give priority to not loosing his king to a KC, over checking blue. He should just move his king or block the threat by the blue B, or check Green.


Why can Red not move his N? The example shows a situation where there is no danger in moving the N. It should be up to Red to decide if he wants to move his N or not. 
Let's say in 2nd pictures red king has no squares left for his king to move and has to move the knight. So, by your rule red has to suicide by moving knight? Seriously? How does this make any common sense in chess?