I doubt that you have a mixed admin. It's more likely that you are initially loading the admin from your upgraded site, but the configure files then cause the links to point to a different version elsewhere on your server. You said that you updated the configure files to make them work in the test environment; but didn't mention changing them again to make them work properly for the live site.
Your images not appearing could also be due to the configure files not pointing correctly to your images directory in the live site.
Could you take a look at your admin URLs and image URLs and post them here?
The message that you appear to have the latest version is telling you only that your database is up-to-date. The problem lies in your code set.
What I meant by it being risky to copy all these files about is ... well ... you're experiencing it. When you move files there's a risk that some don't make it, get corrupted or, since you've changed the location of your site, pointers get missed so that files are no longer where they're expected.
That said, using FTP to move files about on a server shouldn't cause any particular problems. I do it all the time with FileZilla and have yet to experience a single problem. That's why I believe that this is most likely about where your configure pointers are looking for them.
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