Things got sorted out, kind of. I mailed HR about pensions and overtime fees (cf stupidly long hours) last week, and I got their answers (in person, actually) a few days ago.
As for the latter, “nope”. The reason being that apparently my employment contract is (from a legal viewpoint) performance-based, eg I’m not hired on the hour, instead I get paid for the job. Oh well, I guess it’s time to actively organize my schedules into acceptable shape and also start playing around with stocks.
As for the former, the news were great. It turns out that Japan and Hungary have some kind of welfare agreement in place, meaning that if I pay in my pensions here, I should (in theory) get pension even in the unlikely event of moving back to the homeland. I still have to look up what agreement that exactly is and what other countries it applies to, because I’ll adjust future planning to that.
Also, I got excepted from said payments for another year. It’s this smart Japanese system that allows you to push out having to pay until you’re 30 or your income passes a certain limit. It’s more than convenient for me.