Munich to Salzburg day trip - can be done with a Bayern-Ticket for 27€ for two. No train commitment.
Munich to Prague - with advance purchase of tickets, you can take the direct Bahn IC bus in 4½ hours. Best fare is 58€ (29€/pers). Have to commit to a specific bus. Also possible to do by train for less than 40€ for two in 6 hours and no train commitment. Use any of three or four direct trains per day. Buy a Bayern-Böhmen ticket, 30,50€ for two from an automat in Munich. That ticket will take you from Munich to Pilsen, where you can purchase a Czech Rail ticket for about 3,60€/person.
Prague to Berlin - there is an EC every two hours from Prague to Berlin. If you can commit to a specific train, Savings Fares of 39€/person are possible. Using the stopover function on the Bahn Query page, you can specify a stopover in Dresden in two hour increments, but you must take the scheduled train from Dresden to Berlin.
Total price for these tickets is less than $200 (~150€), for 2nd class, which I have never found to be a problem. You are only talking about 3 days of travel, but the least expensive Eurail pass is for 5 days in 1st class (@ $710). That's an awful lot to pay for convenience and flexibility.