Hey everyone.
Question, can you do this route with a four-day pass?
Amsterdam to Copenhagen. With a stopover (of about 5 hours) in Hamburg.
A few days later from Copenhagen (directly) to Berlin.
A few days later from Berlin to Prague. With a stopover (of about 5 hours) in Dresden.
A few days later from Prague (directly) to Amsterdam.
I hope you get it! And thanks in advance for your answer 
Sure it's possible. On a pass day you can board as many trains as you'd like. Simply note that some journeys will be quite long, especially Prague - Amsterdam (12h).
To save time I'd consider the night train from Copenhagen to Berlin : either the one run by SJ or by Snälltäget. Book in advance (you only pay the couchette price) through the railway company.
There's also one from Berlin to the Netherlands/Belgium run by European Sleeper. :)
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