No, that doesn't make sense. You'd need to preface the sentence with Being to have any chance of being understood. But anyway, don't.
Yes, there's no contrast there. That's a very unusual use of the pattern, but I can't say it's incorrect.I've also found this example: As smart as she is, she is equally funny. (Huffington Post) Is it correct? I see no contrast here.
Yes, that's a decent example, as it shows the contrast nice and clearly. Still, I'd prefer it with though in place of as.

Student or Learner