Issues Booking Night Train from Prague to Budapest

That train is a EuroNight operated by the Hungarian MAV. Book at www.nightjet.com or at https://www.mavcsoport.hu/en.
And hurry - the train on 14 december is already fully booked.

BTW, irregularities in the operating times of night trains are nothing unusual. It may be that the train is simply cancelled on your specific travel date, e.g. because the line is closed that night for trackworks.

Rather than leave at 0040 try the train which leaves at just after 2200 from Prague.

The 2 trains attach to each other at Breclav, thus arriving at Budapest at the same time. But you get nearly 3 hours more sleep than on the later section of train, as the 2200 waits at Breclav for nearly 3 hours. Generally the earlier train seems to have better availability.

A section of your train (day cars) will be shunted off and terminated at Breclav, and then you will be shunted on to the 0040 train, plus another train from Warsaw.

New schedules and pricing for night trains after 14 December apparently haven't been published yet.
Keep checking back.

When they are published. Check the prices on the Czech and Hungarian site. Prices might be different, but if the Hungarian site is only a few Euro cheaper, I would stick with the Czech site for the peace of mind of local customer service.

Also, download the train company app and use it to display tickets to the conductor.

Welcome to Budapest and the Nyugati pályaudvar. Constructed by G. Eiffel, and opened 1874. The M3 metro and the 4 and 6 trams stop at the station.