Saving Fare tickets go on sale at the lowest price 92 days before the day of travel. As lower priced tickets sell out, the price goes up. They are only available up to the day before travel, but by that time, most of the lowest priced tickets will be gone.
Saving Fare tickets are only available for connections that include a train of the Bahn (ICE/IC/EC) or the IC bus. The trains between Nürnberg or Munich and Prague are all regional trains, so the Saving Fares do not apply. Fares on the IC Bus start with bus specific, non refundable fares at 19€ from Nürnberg or 29€ from Munich. You could go to Dresden and take an EC to Prague, but that would be round-about and probably longer. You didn't say where in Bavaria.
There is one pass for the three states of Sachsen, Sachson-Anhalt, and Thüringia. There is also one pass for Brandenburg, and it includes Berlin.
If you get a full fare ticket from Prague to Berlin (67,60€) you could stop off in Dresden for as long as you like (well, at least several days). If you get a Savings Fare ticket (starts at 29€) you have to build in a specific stopover time when you book. Both the trains from Prague to Dresden and from Dresden to Berlin will be specified on the ticket, and the ticket will only be valid for those trains.
" If so, how do I do this?"
Go to the Bahn Query webpage and put in Prague to Berlin, departure date and time, and enter Dresden as the stopover. Enter how long you want to stopover in Dresden (300 equals 3 hrs). The Bahn will offer you a Savings Fare for that long a stopover in Dresden. You will have to be on the departing train from Dresden at the specified time. If you want more flexibility in Dresden, go to" modes of transport" and uncheck ICE and IC/EC from the possible trains for the second leg, Dresden to Berlin. This way you will not be held to a specific express train from Dresden to Berlin, but will be allowed stay as long as you like in Dresden and to take any regional trains on the specified route to Berlin, as long as you get to Berlin by 10 AM the following morning.