If the person is entering Hungary by train from a foreign country and does not have a train ticket, can he buy it on train as soon as the conducter aproaches, without any extra fee or penalty (will he pay regular price)?

MÁV says: "If you get on the train on such a station or stop where there is no ticket sale, the conductor will sell you the appropriate ticket without any supplementary fee. Make sure you have a valid ticket before you get into a train or train car without conductor (the letters KN indicate it)."

I think that means if you take off on a station where you cannot buy hungarian ticket, you can buy it from the conductor.

In international traffic you have to hold an international ticket for the whole uninterrupted leg of your journey. So if you don't change trains in Kelebia, you have to have an international ticket, not a domestic one. Of course it is not always easy to check who arrived with the internationak train and who's been sitting already at the station when that train arrived, but if you're not lucky, you'll be fined.

The Kelebia ticket office is closed at night, in that case you can buy a domestic ticket on board the train. But again, remember the above rule.