Thank you, Josh, this really did clarify it here. :)
I noticed the move of header as well, and it was more like I originally thought it should be. I may have followed that library a bit too much, because some place I noticed array() was put as the parameter for $query, but that won't work for post operations.
Finally, I get the structure of things... :)
PS! Do you always have to use id's? I just linked customer by e-mail to the order, and that works out of the box, even though the documentation says ID here as well. I just thought if SKU and email are unique, it's simpler to "remember", but my app will normally work with IDs as these are the primary keys, I suppose. :)