Not true. In fact, Blu-ray doesn't even support 1080p30.
They can output at 60Hz, yes. But since the second generation(?) of Blu-ray players, they can send 1080p24 straight from disc to screen if the TV supports that input (and a 120Hz model should, with appropriate frame duplication - just turn off the "smoothing" interpolation).
Only the case for movies that were shot on film and put on Blu-ray at 1080i60, which are a minority and typically low-budget/foreign releases. The standard format for movies on Blu-ray is 1080p24. You can check this thread for in-depth technical details on specific releases.
I believe that answers your other questions too.
Not true. In fact, Blu-ray doesn't even support 1080p30.
They can output at 60Hz, yes. But since the second generation(?) of Blu-ray players, they can send 1080p24 straight from disc to screen if the TV supports that input (and a 120Hz model should, with appropriate frame duplication - just turn off the "smoothing" interpolation).
Only the case for movies that were shot on film and put on Blu-ray at 1080i60, which are a minority and typically low-budget/foreign releases. The standard format for movies on Blu-ray is 1080p24. You can check this thread for in-depth technical details on specific releases.
I believe that answers your other questions too.