Discounted tickets in Germany and Austria, at least, come in two varieties.
First are the advance purchase fares for long distance trains. These ticket must include at least one leg by a long distance train of the Bahn (ICE, IC, or EC), sometimes of the national rail company of another country, such as an Austrian Rail Jet (RJ). The tickets require advance purchase of at least one day, but go on sale at the lowest prices (usually 29€) 92 days in advance. The prices are tiered, and when all of the tickets at the lowest price have been sold, the price goes up. Thay are called Savings Fare or SparPreis in Germany, SparSchiene in Austria.
These advance purchase tickets are specific to the long distance trains shown on the ticket and are non-refundable. Exchangeability is limited and there is a cost penalty if you do change them.
Generally, the tickets are for connections completely within the country that sells the ticket or with the start or end in that country. Sometimes, but not always, changes of trains are allowed outside the country.
Second are all-day, hop on/off, regional and country-wide passes for regional trains (such as the Bayern-Ticket for Bavaria or the Schönes-Wochenende- or Quer-durchs-Land-Ticket for all of Germany during the week or on weekends, respectively). There is also the similar Einfach-Raus-Ticket for all of Austria. These tickets are a fixed price (dependent on the number of travelers (1-5 in Germany or 2-5 for the Einfach-Raus-Ticket). there is no need for advance purchase; you can buy them right up to train time for the same price.
These tickets are shown on the national rail companies schedule and fare pages, http://reiseauskunft.bahn.de/bin/query.exe/en for Germany and www.oebb.at/en for Austria.
In your case, I don't see any discounted ticket for Lauterbrunnen to Salzburg from the Austria Rail website, but the German Rail site shows a ticket via Zürich and Munich for 138€ for 2 people vs 331€ full fare, a savings of 58%. There is also a 98€/2 ticket available, but it uses the Bahn Intercity bus for the Zürich to Munich leg; I'm not sure how you feel about that.
Do the day trip from Salzburg to Hallstatt RT via Attnang-Puchheim and Bad Ischl for 33€ with a 2 person Einfach-Raus-Ticket. You will need to to use regional trains between Salzburg and Attnang-Puchheim; the rest of the trip is only regional trains.
You can get Salzburg to Vienna from the Austrian Rail site. There is also a low cost train called Westbahn for that route.
You can get Vienna to Munich for 68€/2 from the Bahn. One day (2 nights) is enough time only for Munich itself, but if you must go outside Munich that day, use a 28€ Bayern-Ticket.
I see Munich Hbf to Frankfurt (Main) Hbf tickets for as low as 58€/2. If you stay in Mainz you can buy a Rheinland-Pfalz-Ticket (regional pass) for 2 people for 29€ to go from Mainz to the Rhein gorge. From Frankfurt, you'll need an S-Bahn ticket to Mainz (28€ for a group day ticket - Gruppentageskarte and the RL-P-Ticket. Alternately, but a Gruppentageskarte for Frankfurt Hbf to Bacharach Bhf for 44€ (covers RT for 2 people), go to Bacharach, take the boat trip to St. Goar, then come back on the train to Bacharach with a full fare ticket (7,60€/2), then use the Gruppentageskarte back to Frankfurt.