The local train from Rothenburg Station to Luzern is included, bus travel isn’t.
You just do need to show your railpass.
When going by bus, you’d need a normal ticket.
Buses are not included. Trains would be but if you’re only going to Lucerne it won’t be worth using a pass day. Of course if you’re going further it will be good value.
A day pass for Rothenburg - Lucerne (Zone 10) costs 9.60 CHF full fare. It includes unlimited travel on buses and trains in that area. Network map : https://passepartout.ch/liniennetz-tarifzonen/
Seat reservations aren’t a thing in Switzerland, whether on regional or long-distance trains. Simply log (on Rail Planner) the train before boarding, hop on and sit wherever you want. Train ends are generally less busy.