Ivan G
This is coming next, you will have a new button on profile tab 
Unfortunately this is up to a browser whether to foreground a window or not and has nothing to do with BT. Its tricky to find a correct foreground window if...
I think this is resolved in 3.5.2.
I will try a few things, it could be related to the fact that BT is not in foreground when links are opened, not quite sure.
Please try 3.7.1, this has worked for me. I think the issue is BT is disposing process handles too early, and that's only reproducible in the release mode.
This should not be an issue anymore since v4.
The browser itself does not expose command-line arguments to work with tab groups. I think this would need a browser extension to work properly.
Sorry, not possible at the moment in any browser.
I assume you have tried this and it doesn't work for you? I like the idea of adding rules that must always trigger the picker!