"They are eating breakfast with us."
Translation:הם אוכלים איתנו ארוחת בוקר.
How important is word order in this? Is "הם אוכלים ארוחת בוקר איתנו" not correct?
It's correct but less natural. There is a natural word order and some accepted variations, your suggestion included. But it sounds like you want to emphasise that they are eating with us, as opposed to with someone else. הם לא יכולים לאכול ארוחת בוקר איתך, הם אוכלים ארוחת בוקר איתנו.
Because עמנו isn't correctly spelled. Should be איתנו. Also see the other comments about word order.
Ah. I thought it was out of use. Seems its still used quite a bit. Your question about word order has already been answered by AlmogL anyway. I asked the same question.