Are there mobile fingerprint readers? (For EES, I mean). If not, it’ll have to be all non-Schengen people off.
At Metković in Croatia, they're carried out onboard with mobile fingerprint readers. It's a bit of an absurd situation, because Ploce could easily host entry and exit controls for both Croatia and Bosnia, skipping the Metković stop. A local Ploce-Metković-Caplinja train could easily operate in lieu of the Metković stop on the Sarajevo train, but Croatian Railways is remarkably uninterested in connecting the local Croats.
Of those, the Budapest-Belgrade is probably the biggest passenger flow? I can't imagine turfing everybody out at the border will be popular. Maybe they'll have juxtaposed controls?
I don't think they will, as there will be intermediate stops at Novi Sad, Subotica and Szeged as a minimum. It would actually make sense to implement full juxtaposed controls on this route, but I can't imagine there's any will to do so.
It's done both ways: Chop has a full border crossing in the station, so passengers are either cleared in the station or onboard the train, depending on the origin and destination. At Zahony, the controls are onboard the train.
At Premysl, EES and Schengen checks are done at a building on platform 5.
The international station was out of use for a while, but it was brought back in after the start of the war. Having said that, this is only for passengers arriving/departing at Przemyśl, trains only making intermediate stops simply have onboard checks.
With the Ukrainian stop at Mostyska-2, I believe that this is largely because there isn't an agreement between PL and UA to return any passengers who are denied permission to leave Ukraine, so the only option is to carry out the border check there rather than in transit between Lviv-Przymyśl. It's a stupid situation and should be solved by having juxtaposed controls in Przemyśl, but there's no will on the part of either country to implement them properly. The same story repeats itself all over the PL-UA border, unfortunately.