Hi! Eme.
How about Ver.4.0 that accepted your request?
I hope you are satisfied.

-Badges
Common customization can be set collectively by ".spc-badge".
Please refer to the example on the options page.

-Tooltip
You can customize everything in CSS, including where and how it appears.
You can also erase the default ones and make your own.

-Automatic balloon disappearing.
If the automatic display is annoying, you may want to set "Opening behavior" to something other than Auto.
You can also toggle with the Shortcut key.

-Folder
You can use the "Show last used engine first" feature.
It is recommended that you use CSS to display subfolders in exactly the same place as the folder icon.
See the options page for examples that might be helpful.
In addition, all icons can be changed with CSS. (Including folder)

-Folder checkbox on options page
The folder checkbox is a toggle button for the engine directly below (not below).
This is explained in Tooltip.

-post method Search
The process up to now did not work on Microsoft Edge(Chrome), so I changed it, but it seems to no longer work on Firefox 72.
Firefox Nightly (74) did not notice because it works without problems. It looks like a bug in Firefox (https://bugzilla.mozilla.org/show_bug.cgi?id=1344465), but I will fix it.
Thank you for letting me know.

Version 4.0 is designed to allow you to customize almost all of the pop-ups with CSS.
Maybe I could write more CSS examples, but I don't have time. This is the limit.
We are considering creating a wiki that users can edit freely and linking from the options page.