tab group into new window

Is there any way to implement a feature to move/open a group of tabs in a new window? Or join windows (with several tabs) into one single window with several group of tabs?

That's different functionality than this extension offers. You may want to have a look at the TabMixPlus extension for that.
I can confirm that the combination of the two plugins works just fine.

I usually use Multiple Tab Handler for that. You can select multiple tabs and drag them to another window.