Om is the preposition used for talking about distance in time to a future event. In this case the other prepositions have other meanings.
- De betalar i ett halvår = They pay for half a year
- De betalar på ett halvår (colloquial) = They pay (off the loan) during half a year
- De betalar om ett halvår = They will pay half a year from now.
why won't "They will pay half a year from now" be De ska betala om ett halvår
It's just that we have several ways of speaking about the future in Swedish. We often use the present tense, but both ska and kommer att are possible, too.
Does this mean they pay continuously and are only done after six months or does it mean they wait until the end of the six months to pay? Or does it not matter?
what would 'they pay every half a year' be? Because I had that and I don't see why it would be wrong...
Right. Or De betalar en gång i halvåret. So it's a very different meaning. om ett halvår means that it will take half a year from now until they will pay (once).
It's a perfectly normal expression meaning 'once per …', just like en gång i veckan means 'once a/per week'.
I think the point others are making and with which I agree is that the sentence requires context to make sense.
Which sentence, the DL English translation or the original Swedish sentence?
I suspect the Swedish is clear enough.
On the other hand, the English word "in" can be ambiguous. Compare:
1. I drove to Paris in one hour.
2. Our trip to Paris begins in one hour.
In 1, "in" refers to how much time the drive will last.
In 2, "in" refers to how much time will elapse before the drive begins.
But even in English, you may not need any more "context" than the rest of the sentence in which the ambiguous term appears.