Bayern ticket from Nurnberg to Salzburg? Can you use it all the way through?
You can use a Bayern-Ticket as long as you stick to regional trains. There are regional trains that run on the same tracks as the fast ICE between Nürnberg and Munich, every two hours as I remember. From Munich to Salzburg, you can use the Bayern-Ticket for the hourly Meridian regional train.
Salzburg is considered a "border" station for German Rail tickets. You can use Bayern-Tickets, German Rail Passes, and other German passes on the line into and out of Salzburg.
Yes, you can purchase a Bayern-Ticket in advance online, but other than having it in hand, there is no advantage. The price is always the same (€2 more at a ticket counter). Pick it up at a ticket machine at the station the day of travel.
You can also buy Bayern-Tickets at the Salzburg Hbf - for sure from a German Rail automat (there are some on the platform) or from an Austrian Rail automat (I have seen BTs at Ausrian Rail automats in Austria).
Not sure which option better from Nurnberg to Salzburg
If you want to go by express train for either of the legs, the rail pass option will cover the train. The Bayern-Ticket option will take longer but cost less than a day of the rail pass and allow you to save the rail pass for another day. However, you must use slower regional trains.