Find the answer to your question
Why does the Finding Service not return items on my site?
for example: My site is UK, but I want to find items which ship to the US only. Why can't the Finding Service find these items?
The answer is that when an item is specified only to ship to specific site, in our example US, then a search on a site where the item does not ship to, would not surface this item. This is by design, since most people searching on a specific site, would only want to find items that they would be able to recieve.
So from our example:
Only items shipping to UK should surface in search on the UK site on the Finding Service.