PUZZLES : ANALYSE WHAT SHOULD BE PLAYED WHAT NOT

 IN this position, white is threatening mate at h7 with Qxh7#. But its black turn to move. He can block the bishops diagonal with either 

a) ......Ng6

b) ......f5.

c) ......e4.

Which one is good move, which one is bad? How will the game continue in either case?

 In position below, white has just played Qh5, Black king should flee to f8, (why?, if its whites turn here, how will he mate black king?)

 but instead black plays .... Ne7, which is a mistake. Why?