There currently is one option to travel by night train from Prague (Czech Republic) to Copenhagen (Denmark), taking between approximately 13 and 14 hours: Namely the RJ 386. These lines are operated by Deutsche Bahn, České dráhy and DSB.
Deutsche Bahn (DB) exited the actual night train business in 2016. However, it operates around a dozen Intercity and Eurocity trains that run exclusively at night.
In these night trains, there are only first and second class seats. The lights stay on all the time and there is no way to recline the seats.
ČD, the Czech national railway, operates domestic and cross-border passenger trains linking the Czech Republic with its neighbors.
DSB, Denmark's national railway, runs passenger trains throughout the country and connecting services abroad.