MAV App for buying the tickets? Go to the website and see how your luck holds out. I buy tickets on line quite often, then they transfer to my phone App. https://jegy.mav.hu/jegy/vonat
For your trip I checked the MAV site again today.
For all of October the rates are current and working. About $25 Prague to Budapest.
But you indicated you would be returning in November and the MAV site hasn't posted updated November ticket prices yet. Yes, you can still buy a ticket and there are prices shown, but they are goofy high. In a week or two they will be the same as the current prices for October, about $25.
i suspect you will end up buyng from the Czechs, thats fine. Which ever, do download their APP. I presume the Czechs have one. Makes displaying your tickets on the train much easier.
Having said all of this about trains from Prague to Budapest, if the timing works, it a lot faster to fly. And if you travel light doesnt have to cost much more. I did all the math once including travel time to and from airports and train stations, early arrivals etc and you save about 3 hours on the plane. And if you consider that maybe the first hour in the airport isnt "early arrival" its breakfast, then it saves 4 hours.
Also check RegioJet. The will use Kelenföld Station in Budapest, but thats not the end of th world. Its on the M4 metro line. I looked and they have prices up for October and Noveber. Doesnt look cheaper than the national companies, but check out what comes with the ticket. I understand it can be a bit nicer than the national companes. Dont know though. https://regiojet.com/