...but the 'real' compositions on vagonweb.cz are showing that it has run without a sleeper or a couchette.
Well, "real" composition dates Thu 6.2. / Fri 7.2.2014, it was quite long time ago. Maybe then there was some reason why carriages were missing, but as of now MAV website easily allows to purchase ticket+reservation sleeper/couchette
So in this case we would recommend to trust official MAV website, hardly they would sell reservation so easily while knowing that there is no carriage(s) running
Is it possible to buy a 1st class special ticket for this train?
Since there is no "Belgrade Spezial" for 1st class, it's not sold online. But at the station it won't be a problem to buy such ticket (fare should be 42,7 € one-way or 48,8 € return)