You won't know the details of that until you sail - don't schedule something before at least 2+ hours after arrival and of course be back at least 90 min before departure.
No, the casting should be able to be done wirelessly and does not rely on a Voom package. Bring the HDMI to ensure the connection in case the casting doesn't work.
Again, anyone/everyone, even if they don't have a cruise booked, can see the menu you are seeing. It might have some historical value but virtually no one searches for info in old threads.
Somewhat recently, folks have started reporting the denial email being received the day before sailing. The pattern has been that you may get an "initial" denial about two days out (which means that they are done with them shoreside) but on-board upgrade are possible - then the "final" denial usually is received early evening on sail away day.