"Real ducks live in the house."
Translation:В доме живут настоящие утки.
In English putting the word 'Real' at the beginning of the sentence implies that the ducks are only real if they live in the house. As in 'Real men drink beer.' A better word order would be 'In the house there are real ducks'.
The locative дому is usually used only with the preposition на (на дому́) meaning "happening at home". For example, рабо́та на дому́ — a work-at-home job. (To be honest, I can’t come up with other examples.) I think you are right in the assumption that в дому is dated.
You have a typo there. It should be "живут" not "жибут" otherwise that word order also works