I'm located in Slovakia 🙂
I will probably need temporary FTP in order to be able to debug why those links are broken. Navigation items are problematic, as I mentioned earlier. I might be able to figure it out though, and construct some kind of permanent fix to the functions.php file.
The page with the iframe might be more problematic. I've looked it up, but one issue is that the frame URL leads to a password protected page, so in best case scenario the plugin could only extract the “password” word out of that page.
If that is not doable, there is a much simpler solution in my opinion. You can actually enter additional search keywords for each page, on the page editor: https://i.imgur.com/idY1lqf.png
So, instead of relying on the search to parse and find whatever it can, you could simply just enter the keywords to look for into that box – it's worth considering. In that case, you could also bypass using the index table engine, I see you have around 1000 posts, using the regular engine won't make too much difference, I believe.
Anyways, I won't be online too much in the next couple of days (easer holydays), but I will definitely check the support forums when I can. If you can leave temporary FTP access, I will definitely look at it tomorrow, or sunday morning, to see if I can fix that nav menu thing.
PS.: please have a back-up of everything on your site, just in case. I have never broken anything on anyone's site, but it's much safer for the both of us.Best,
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