I don't know if this is covered by the rules, but yes if you succeed at the bluff they think you've lied.
Depending on what you're saying they might get a +/- to their sense motive, so it might end up being easier/harder to trick them.
Yeah, that should be covered by the "Deceive or Lie" part of the bluff skill.
You're attempting to deceive people into thinking what you're saying is a lie, so that should have the same DC and modifiers.
For example, even if Sandra the Shifty acts very suspiciously while she tells you that the sun is bright, your common sense would prevent the deceit from working.
Yup, it's the same as any other Bluff to deceive. You're lying; the lie just happens to be rather meta.