Yes, counters are still open at 10pm, so don't worry. And yes, they located on your left when you enter the building from the main entrance, but not exactly on your left - you will need to walk app. 50 meters straight forward besides platforms, then you will see International tickets sign (it used to be in blue). You can as well enter International ticket counters from the outside, if you'll use left wing entrance (in case you stand in from of the main entrance) to the station.
Cashiers don't speak English fluently, but will be able to understand you, especially such simply things as destination of your choice. No problem to buy ticket for the next morning. Most international tickets are valid for one or even two months (unless you need seat reservation for specific train), so they probably won't even ask the date of departure, but simply issue ticket from today
It is not that hard to interpret your ticket (will look like this -
http://www.railfaneurope.net/pix/hu/ticket/01_024b_Budapest_ZahonyGr.jpg), as you can see it is clearly written "from" ("von") and "to"(nach), in the lower right corner you can see fare in Hungarian forints (sometimes in euro as well), other things aren't that important for you.
Just when you enter the station you can huge screen showing all the trains and platform number, so no problem to find yours, especially at 5:30am.
During the day there are special rail stuff checking your ticket before they let you to your platform, but during late evening and early morning usually there are nobody there. Afterwords the only person you will need to show your ticket is train conductor, he/she will be in MAV uniform. If it is sitting carriage, then they will come after train departs, if sleeping, then conductors will be standing near one of the wagon doors.