Is a german rail pass valid on all the local trams and busses, etc, needed to get to the castles, or do I also need to purchase this "Bavaria Ticket?"
A German rail pass is only good for railroads which include the S-bahns in cities, but not U-bahns, trams and buses. The Bavaria ticket (and tickets for other German states) includes all local transportation and the slower regional trains, but not the faster trains such as ICE.
In this case, you would just need to purchase the bus fare separately or take a taxi as they aren't that expensive for the short distance involved.
a) a German Rail Pass for Munich to Füssen by train plus buying a return bus ticket (cheaper) for the short bus trip from Füssen to Hohenschwangau.
b) the Bavaria Ticket (EUR 19,00 for 1 person, EUR 27,00 for 2-5 persons)
2. covers the bus from Füssen to Hohenschwang and e.g. also the trams and buses in Munich
On weekdays (Mo-Fr) only valid past 9am.