Glad that you like it :-)

Possible features/changes are listed in the page at https://github.com/webextensions/live-css-editor/blob/master/TODO.md

External window:
Implementing that would be a bigger change. There is an existing workaround which can solve the use-case of editing in responsive design view to an ok-enough level. You can use the feature "Watch CSS files to apply changes automatically" and follow the instructions there to set it up. After that, open your file in any code editor and edit it. You changes would reflect immediately.

Providing light/dark theme:
That may need an alternative copy of the icons and the UI for it. Since that is extra effort, I'm currently lazy about it ;-)

Changing the background color to neutral dark-gray with appropriate shadow:
That can be done.

I've added your suggestions in the TODO file mentioned above, but may not be taking them up soon due to other listed priority tasks or time constraints. PRs are welcome :-)

This is pending for the Firefox version of the extension due to Firefox bugs mentioned at https://github.com/webextensions/live-css-editor/blob/master/TODO.md#improvements

There is scope for adding some sort of workaround. That may be added later.

Glad that you like it :-)

1. Regarding storage - The styles that you type are stored in "localStorage". When you are cleaning the history, you may just uncheck the "Offline Website Data" option in the "Clear Recent History".

2. Regarding taking too long to load - This is partly an issue from our end because the whole extension consists of so many different files. We can optimize it by bundling the most of the code into just a few files. The reason for not attempting that was the fact that using minified code would make the approval process for Mozilla extension store take longer time. I believe that Mozilla's extension approval process has now become a lot more automated and faster. We may now be able to attempt a fix for this problem by bundling the application code without adding much delay to the update/release process. Though it might take a little time before we make that change.