You can buy so many days you want. There are passes like 10 days in 2 months or 15 days continues. 

About taking trains in the night. When you enter a train before midnight (23:59, scheduled departure time) you use one travel day. If you change the train after midnight (from 0:00) you need a new travel day. 

Example: The Nightrain Intercity Notte from Milan (20:10) to Palermo (Sicily) (16:00) you need only one travel day. 

@Laura di Caporiacco  Maybe you share your destinations with us and we can suggest where to use one of your 7Traveldays and where you maybe use cheap Standard tickets :)

For example i usually buy normal tickets in Czech Republic / Poland/ Slovakia as they are pretty cheap and often cost less as the average value of a travelday ;)

Just as seewulf says. Some trips -that tipical newbees always seem to do-can be quite cheap or at least affordable by buying other tickets. And noone forces you to go by train only-there are also often much cheaper BUSes or even flites. (though these will require advance booking).

@seewulf thank you! my plan was to go to Munich, then Prague, then Berlin, then Copenhagen, and then Amsterdam. The problem is with Copenhagen, which is very far and thus we thought about a night train, which takes us two days for going and two for leaving :// maybe we’ll need to rule Copenhagen out, in the end...

Why you need two days for Nighttrain from Berlin to Copenhagen?

Just get onboard the Snalltoget Nighttrain till Høje Taastrup and then buy a cheap danish public transport ticket to cover the Journey to Copenhagen :)

That way you need just one travelday from Berlin to Copenhagen :)

Copenhagen - Amsterdam would need two traveldays when you start with a Nighttrain from Copenhagen.

But maybe you stop inbetween for few days in Hamburg :D


Plan B to safe traveldays

You start with Munich then onwards to Prague :)

From Prague you transit through Berlin directly to Copenhagen still one travelday when you use from Høje Taastrup to Copenhagen a danish ticket :)

After your visit in Copenhagen you catch the Nighttrain back to Berlin  (1Travelday)

and visit then Amsterdam with one travelday from Berlin (every 2hrs a direct Intercity)