Thanks Stephanie and Dee Raven for your answers

By the way, I need your help with this exercise:  Which one is correct?

1/ Ann: "Must we do it now?"     John: "No, we__________"

        A/  Mustn't                B/ Needn't

2/ A/  What do you do for a living?

     B/  What do you earn for a living?

I think "like" has an underlying meaning of "in the manner of" so your first example works well. 

For the second example, it should read "she doesn't work as hard as she did." And I would say that "as" has an underlying meaning of degree or quantity (comparison).

So if you were to say "Sly like a fox" that would mean sly in the manner of a fox, vs. sly as a fox, meaning sly to the same degree as a fox. So there is a slight distinction between like and as. In my opinion.

Hope that makes sense. 

Yes, I think you've got it! 

As for "maybe" and "perhaps", I really don't see much difference, except that "maybe" is more commonly heard and less formal than "perhaps," which is found in more academic writing.