The preview links are these:
I suspect you are running some sort of page caching which is how these links are being shown publicly. The page was cached while you were editing it. And now those cached links are being displayed publicly.
I suspect it is the same reason the other links are not working correctly. The page cache is showing the same cached paged vs the page it should be showing.
What ever you are using for page caching, try flushing it.