Monads can be likened to objects, and classes of objects, and classes of classes (meta classes), that are familiar enough (even if not totally accurate), that they would be accessible to many more people who are already familiar with these concepts.
Yes, or like Aspects of AOP: an organizational unit of behavior or functionality. If you approach them from the software engineering perspective and not from the theoretical CS/mathy perspective, one rough way to think of them is as overloading the meaning of the semicolons that separates statements.
Regarding coming out straight, I'm really not sure what to say. Some people who talk enthusiastically about Haskell come from a different background than advocates of many other languages you're familiar with, and that's part of why they take some things for granted and stress others. My own experience hasn't been easy, but it certianly hasn't been that somebody's evasive or dishonest about the design goals. So if you read Wearing the Hairshirt or Tackling the Awkward Squad, for example, I don't think you get the sense that somebody's bluffing (well, I didn't!). Sure, uncontrolled effects are presented as a bad thing, but part of what's good about monads is that they let you tag the bits that are and those that aren't pure, and the typechecker doesn't let you mix them incorrectly.