Straightforward question: Is it dangerous to use auto sensor cleaning when the lens is attached?
No. It's fine; I can't imagine why there might be a problem. Automatic sensor cleaning generally works by shaking the sensor a small amount at high frequency. This doesn't get anywhere near the lens (at least, not more than the sensor already is). I guess it's mildly possible that some dust might end up transmitted to the rear element of the lens, but that's okay — that's easily cleanable.
Many cameras can be set to (or even defaults to) automatic cleaning when the camera is turned on, or off, or both. It's difficult to imagine that camera makers expect no lens to be mounted at this time (in fact quite the contrary), so we know for sure that it's designed to operate this way.