Dany, you have come up with some thoughtful improvements! I consistently find myself toggling between execution, window size, run-time position, and documentation, and this would make that navigation MUCH easier.
Kudos! I was going to post this idea today, but found this old post and didn't want to duplicate. I think changing the dialog to make it the same or similar to the LabVIEW options dialog is a very good idea. In the process, the number of categories could be reduced. For example, with a larger dialog, all of the windows properties should easily fit on a single page.
Also, with so many window options, perhaps a menu for selecting saved window configurations? The window configuration selector would come with "Dialog", "Application", etc,. out of the box.