Thank you. It's probably possible by adding a script to all web pages that listens for such input, but that's not a great situation. This add-on is also practically in maintenance mode. In the recent years I've only been addressing reported bugs rather than developing new features, which is likely to continue to be the case.

Thanks for using my extension! I appreciate and have considered your suggestion, but I won't add it.

This feature would essentially only remove the step of opening a new tab of the selected page. Since this only takes two mouse clicks (click URL bar to select it, drag selection to tab area) I don't think it adds much value on its own.
I considered the possibility to clone a tab including its state, meaning for example keeping text input in fields, but I've looked into it and it isn't possible.

There is a setting in the Workarounds section to add/subtract pixels when calculating how to place and size popups.
For example: if you have a rule that sets x=0 and width=100, and use this setting to add 10 to X and subtract 20 from the width, the result simulates a 10 pixel gap on the left and right sides.

Note that this only applies when the popup is opened and placed by the extension, **it's not possible to add a real invisible border** to a window from an extension. If you use for example Windows Snap afterwards then the popup will not have a gap between itself and the other window.

Edit: Sorry, I still don't understand what you are asking for, can you clarify? This is what I refer to as "invisible border": https://i.imgur.com/3fEz63K.png (It's only a problem in Windows 10 as far as I know)
(Edit 2): Maybe I understand... Do you mean the title bar that's supposed to be to the left of the minimize/maximize/close buttons but is gone in your image? That's not something I am explicitly able to hide, and I don't want to add features that relies on bugs in order to work.

Integration with TST: It looks possible, they provide an API this add-on can use to do this. I'll have to consider whether integrating with other add-ons like this is something I want to support, but at the moment I'm leaning towards not. I've created issue #40 on my github repo to track this request.

Dragging to edges: This is a Firefox bug, I'll have to refer you to their Bugzilla for this. I did not find an existing bug when I did a quick search so you might want to create one.

This is unfortunately a limitation set by Firefox. The domain URL is shown automatically in an effort to combat phishing.
If you want this behaviour changed you can make your voice heard on this bug: https://bugzilla.mozilla.org/show_bug.cgi?id=1296365

* I've edited my reply as I misread the proposal in that bug, my apologies.