I'm not sure I understand the suggestion. What are you referring to as the "standard menu"? The menu below?

Available in 7+ Taskbar Tweaker v5.3.

Fixed in 7+ Taskbar Tweaker v5.3.

7+ Taskbar Tweaker v5.3 was just released, with full Windows 10 Creator Update support.

I've changed it. I'll look at it when I have some spare time.

I could reproduce both issues with Notepad, too, so they are not specific to Chrome. The second issues has a similar cause: because of the ungrouping, the chrome icon on each virtual desktop belongs to a different group, and thus the ordering is not preserved.

To solve these issues, the ungrouping option has to be reworked to adjust multiple virtual desktops. I'll try to look at it once I have some spare time.

That's supported since v4.5.7 (February 26, 2015), with the no_start_btn_spacing advanced option.

Bug 2: I could not reproduce the issue. Can you provide exact reproduction steps? A video demonstration can help, too.

Bug 1: I could reproduce this. What happens is that all of the virtual desktops share common data, and that makes things tricky for 7+ Taskbar Tweaker. The decision of whether to group a newly created button depends of whether the existing button is only a pinned item, or contains a button. In your case there are two virtual desktops, and while the existing item doesn't contain buttons in the current virtual desktop, it does contain a button in general. That's why the grouping doesn't take place.

I might look at it one day, but currently it's not a priority.