Encore is the authoring app in the suite. Internal or external shouldn't matter.
Steve Jobs hated BD burners, so the plain answer is no, at least not internally. Maybe with some hacking of the OS and ... it may be possible, dunno.
Yes. You can get an external burner (OWC/MacSales sells them), and burn BRD from Encore on a Mac. You could conceivably install a "raw' BR burner (Panasonic is a manufacturer, and is the guts in the OWC external I have.) in the spare "optical" slot of a MacPro. And yes, you can use 10.6.8.