So, before I start I must let you know that I disabled the WordFence plugin temporary. I think it was running some kind of scan task or something and it might have brought your site offline, I'm not sure though. You can re-enable it later on to confirm this. It might just had been a brief server outage after all, I don't want to blame anything.
1. That's what it does. It can't change your results layout, it changes the actual results you get (unless they are the same as the default). Changing the results layout is unfortunately only possible by editing the theme's search.php (or corresponging) template file.
2. You can't have both with a single instance 😉 Why don't you create 2 search instances, one of them you will use in the mega menu with the hover layout, and the other one as a block.
3. There were some nasty styles implemented (coming from the theme I guess) which enforced padding, margin and color on the search boxes. I put some magic into the plugins “Theme options” -> “Custom CSS” box which enforces the correct style exclusively to the search boxes, so it should be all right now.
4. You had the TEST category excluded, and the Banana post was belonging to the TEST category, that's why it didn't show up. The others weren't showing because the fulltext search was enabled (while it was disabled on the settings, it beats me how), but I saved the options again and it's showing now – perhaps some values were lost at the time of the server outage. The “Toothbrush” result is not showing because it's still a draft. Once it's published it will show as well.
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