What is blacks's worst possible move here (except Ke7 ) : a) Qe7 b) d6 c) Bd6 d) f6 e) d5 ?

I'm guessing you want us to answer that the opening whose name is the title of this thread is the worst. It certainly has the worst reputation, and it doesn't defend the pawn, but I've never personally looked into how well it would if played as a gambit. (1. e4 e5 2. Nf3 f6 3. Nxe5 without 3. ... fxe5)

In your multiple choice, I don't know why you list d6 and d5 as possibly bad moves. 2. ... d6 is the Philidor Defense, which is a very good opening. 2. ... d5 is the Elephant Gambit, which is very playable at amateur levels, though probably not quite good enough for master level play.

--Fromper 

The Damiano Defense is a bad way to defend the pawn. Damiano and Greco analysed it as inferior in the 1590-1620 period, and I don't know why the Damiano is named after him.

I will quote Graham Burgess on the Elephant:

"Until recently, this was considred just a bad way to lose a pawn, as black lost to much time with queen captures." The current best try for black is 3. ... Bd6, aiming to mobilize the kingside.

Hope this helps,

Eric

We name openings after people whom made them popular like the Réti Opening, Benko Gambit, Grünfeld Defence and the Philidor Defence. As ironic as it is, Damino said 2. ... f6 is the worst defence but because of that we named it after him.