Hrqls:
Is the K13 group dead? No. If black tries to invade at L13, white would play at M13. Now, black cannot play at L12 or N13, as it would be suicide. The L13 stone is dead and white lives in that area. If black invades at M13, white plays at L13 and a similar thing happens.

Is the M6 stone dead? Yes, if it were played out, white could capture the black stone. But white cannot make two eyes in that area enclosed by black. Since two eyes are the minimum requirement for life, the white stones are dead. It is in white's best interest to not capture that black stone, as white needs to play more than one stone to capture a single stone; the net outcome for white would be less than just declaring them dead.

If white plays at A and black plays at B, white *cannot* play to the left of A. It would be suicide because the black group still has one liberty to the right of B. This is the same situation as the K13 group in your previous question. (except this is straight 4 versus bent 4)