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.
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?