Does "whenever / whether" equals to iff? I encountered a question that goes like this:  
M is a TM that accepts w^r whenever it accepts w  

which of the following does it mean?
 M accepts w^r <->  M accepts w
 M accepts w^r ->  M accepts w
 M accepts w ->  M accepts w^r 
same question for whether please.. thank you :)
 A: As already commented, "whether" has no business here. 
Now an idea: when you want to clear out for yourself the meaning of some more or less obscure phrase, try to find out every day words to substitute and understand a little better what's going on.
In this case, let us substitute for example "M accepts $\;w^r\;$" with "I am alive" , and "M accepts $\;w\;$" with "I talk" , so the given phrase is
"I am alive whenever I talk" , and now ask yourself what's the closest meaning to reality: does it mean
== I am alive iff I talk == , or 
== If I am alive then I talk == , or 
== If I talk then I am alive ==.
The first two fall at once when you think of mute people, and the third one is really true. You can try different words/phrases to put instead. 
This is not proof that the actual sense is what Mariano commented, and it could perfectly well be that the author simply mispoke (this happens quite a few times with scientists/authors in general who have not much training in logics. Mathematicians usually go wrong in these matters less than others) , but I think it could be a good instrument for you (and everybody) to check a particular meaning in many cases.
