I am a bit unclear on what the screenshot is showing?
Notepad and Explorer have the OS native tabs replaced by Groupy ones which is why they would not be in a separate bar. If you want that you can disable the option in Groupy to do that.
With regards to the Window rearrange issue, are you able to explain more please. If you are using the option to show only the active button on the taskbar for the active window it would be normal for this to rearrange positions on the taskbar as you swap windows. This is how Windows works. There is the option to show only one combined button which would avoid this.