Correct. Perhaps @Nick Brooke can clarify what happens in the case of Community content products that often become available later as POD
Correct (although the PDF comes from Bit & Mortar, not us)
Correct.
I'd also like to add, that if you buy a physical book from a store that is not Bits and Mortar, and then you persuade the shop to join Bits and Mortar, it's at the discretion of that shop if they want to give you a free PDF retrospectively (there's admin).