Please try 7+ Taskbar Tweaker v5.5.0.7 beta which I just released. It should fix both issues.

You can drag Taskbar Inspector from the gray are and move it to the desired monitor, then it'll display that monitor's items.

Anyway, your screenshot indicates that there's an issue - the gray area shouldn't be that big on the bottom and on the right. I'll check it when I have time for it.

The context menu problem is a result of the following issue:

Dialog does not support DPI scaling

You can try forcing DPI on 7+ Taskbar Tweaker. Here's a guide on how to do it.

The Taskbar Inspector is a completely different issue. It's not related to DPI, since Taskbar Inspector runs from the context of the explorer process, which supports DPI. I've never experienced this issue - can you try to provide a way to reproduce it? Does it happen on every monitor, or only on one/some of them? What happens if you resize it?

Have you tried finding which option causes the problem?

Are there any recorded instances of Taskbar Tweaker creating conflicts with Classic Shell or Open Shell in the past?

No, not that I'm aware of.

Merged with this suggestion:

https://tweaker.userecho.com/communities/1/topics/476-multiple-system-trays

The virtual_desktop_order_fix advanced option is not supported in version 5.5.0.4, due to changes that occurred since insider build 17713 (which 5.5.0.4 was designed for).

I plan to fix it, as well as the other limitations (known so far: some thumbnail-related options and combining options). For now, please disable this advanced option.

It's difficult for me to help with the amount of details that you provided. I will need more information to be able to understand what's the problem.

If you can find a way to reproduce the "sotflock", please provide the steps. e.g. if you notice that it happens when you do specific actions.

Another thing that you can do is try to find out whether the issue is caused by a specific option of the tweaker. Try using the tweaker with all of the options turned off, and see if you still get the issue. If not, try turning the options on one by one to find out which option causes the trouble.

Yet another thing that might be happening is incompatibility with another app. A conflicting app can be another system customization tool, such as a custom start menu.

Also note that you're the only user to report such an issue, so I'm inclined to think that there's something unusual with your system, regardless of whether the issue is actually caused by 7+ Taskbar Tweaker.

The link works for me, so perhaps it's a temporary error. Please try again.

If that still doesn't work, please try it with a web proxy such as this one.

Until it's ready. There's no specific date I can name. See this blog post for more details.

See the following blog post for details:

7+ Taskbar Tweaker for Windows 10 October 2018 Update