When you say you install SketchUcation toolset from the RBZ, and up pops the SketchUcation dialog, do you mean the large main-dialog listing various plugins, OR the smaller toolbar with three icons [red/blue/gray] ?
The SketchUcation toolbar is automatically active when the SketchUcation Extension is activated.
You can deactivate its toolbar it by using the Extensions > SketchUcation submenu entry to toggle it off/on, or use native View > Toolbar-dialog to deactivate the SketchUcation entry, or simply click on its close button... [You'll then need to use the View > Toolbar-dialog, or Extensions > SketchUcation submenu entry to reactivate it (toggle)]
You can deactivate the Extension itself using Window > Preferences > Extensions and un-checking the SketchUcation entry.
You previously said the SketchUcation dialog was opening when you used File > New - I now suspect you really meant the SketchUcation Toolbar ?
It should stay off when deactivated as outlined above...
If NOT, then can you please provide a screen-shot of the flaky behavior ?
Assuming the main-dialog is being flaky...
Whenever you tell us the install SketchUp you skim over the part about 'as admin'...
If you do NOT select the SketchUp installer-exe icon and right-click > context-menu > Run as Administrator - then SketchUp will install with potential weird happenings stored up for later...
Simple being a user with admin-powers is NOT the same, so double-clicking the exe or using context-menu > Run, will NOT work properly and result is weird issues...
Thousands of users of Win 10 and v2016 AND the SketchUcation ExtensionStore plugin have no issues like this, so something is adrift with your set up...
That's why I suspect a faulty SketchUp installation, resulting in subsequent flaky extension installations/operations [not just SCF's]
If you have NOT installed SketchUp by running its installer as the administrator, then I suggest you do the following...
Close SketchUp.
Ensure you have your SketchUp 2016 installer-exe at hand for use later...
Right-click Win 10 icon bottom-left of Windows toolbar > Control Panel > UNINSTALL SketchUp 2016...
When that is complete, use 'Run as Administrator' on the installer-exe icon as explained at the start of this post.
When that's done, reinstall ALL of your extensions/plugins.
The earlier uninstall will have left them intact, but in case the flaky SketchUp has damaged permissions etc, I recommend you start afresh.
Install them a few at a time, and test to see if there are issues...
Report back...
If should not be so difficult