Rail Pass

If you intend on renting a car, I would only suggest that if you plan on seeing a large area from Düsseldorf towards Padeborn. But don't just stop there, you can go to Soest/Westfalen, the oldest city in Westfalen, Münster/Westf., the outlying areas of Dortmund, eg, Dortmund-Hohensyburg for the history site and view, Warburg, even Detmold....all depends on whether you want to track down historical sites.

Using Düsseldorf as a base, you can access a lot of history, including war sites, in that lower Rhine area.

I've been to Padeborn once, took an afternoon day trip there in 2007.

I would advise the train as they are such an easy and relaxing mode of transportation. Rothenburg can be a little tricky to get to as there will be several train changes, but I have done it many times and it is very doable, even for this senior.

The rail pass might not be your most economical option - you can get a cheap advance fare from Duesseldorf to Nuernberg, and all your proposed day trips, plus the one from Nuernberg to Munich, can be done using cheap regional passes. Look at the SchoenerTagTicket NRW for the Duesseldorf area (not to be confused with the national Schoener Tag Ticket) and the Bayernticket for around Munich and Nuernberg. The Duesseldorf-Dortmund trip can be done with an even more local VRR (Verkehrsverbund Rhein-Ruhr) day pass.

and the Bayernticket for around Munich and Nuernberg.

For the day trip from Nürnberg to Rothenburg you should use a VGN TagesticketPlus, €20.30 for two adults and all children. Cheaper than the Bayern Ticket (€32/2) and not subject to the 9am restriction. On weekends, it's valid Sat & Sun, so you could use it for the trip to Rothenburg on the first and to, say, Bamberg the other day.

Website of the VGN (greater Nuremberg transport authority): https://www.vgn.de/en/

For the longer trips I'd compare the price of a pass with prebooked saver fares (Sparpreise). Sparpreise lock you into a specific train, but the same is true with passes as soon as you want to book a seat.

As Philip points out, if you're using mostly the cheap day tickets on regional trains, you have only ONE major journey for which a pre-purchased saver fare ticket (Sparpreis ticket) is needed: Dortmund to Nuremberg.

Cheapest "Super Sparpreis" for this trip is €60/3 assuming "youth" is over 14 (or €40 if youth is under 15) if you can find it on the day at the time you want (seems unlikely.) It could cost a good bit more at this point since these tickets go up in price as they sell.

Schöner Tag Ticket = €46/day for a group x 3 day trips = €138 (After 9 weekday limitation.)
VGN Tagesticket Plus = €20 for your group x 1 day trip to R'burg = €20
Bayern Ticket = €39/day for your group (assuming "youth" is over 14) x 3 days = €117. (Subtract €15 if youth is under 15.)

So your best possible pricing totals around €335 for these 8 days of travel.

Rail passes: Use DB for the best pricing comparisons. Using middlemen like RailEurope will add commissions to your cost. There's normally a sale at DB in February that offers 20% off spring travel for certain passes. Hard to say which passes at this point.

I've got to say, I don't think Füssen (nearly 5 hrs. round trip to the goal of all tourists, Neuschwanstein, for a 30-minute tour) and Salzburg (nearly 4 hours round trip) are particularly good day trips from Munich. Salzburg requires more time, I think. I'd rather spend a couple of nights in Salzburg for sure.