The error you get at bottom is because you are still using a node which has long been deprecated and removed a few versions back. First I would suggest deleting this copy of the project and restoring the backup you made before upgrading. Then fix that node problem by replacing the one you used from VNEngine with this one,
Common > Game Info. Now backup everything again and then try importing the latest version of BGS.
As for those warnings. You should not be getting them, except if you have not been updating for a while. There was a problem during update 0.10 which caused scripts to be detached from objects. See update notes. I explain there how they can be fixed.
If you are unable to click on the icon I show in the image (for update 0.10 notes) then turn the Inspector into Debug mode by selecting it from the drop-down at the top-right of the Inspector. It is a little button next to a lock icon.
The scripts are as follow - just enter the name in the search box of the scripts list window that comes up
For the objects in your scenes, the one you show for example in mage two, you can search for the appropriate script and put it back on. It will depend on what that UI element was, to fix it. In the one your show it seems to be aTextMesh Pro component/script that is not linked. Not sure why a reference to that would be lost, except if you changed from the Asset Store version to the Package Manager version of TextMesh Pro. You may also find
BGS > Other > Missing scripts Finder useful to find objects in the scene that are missing scripts.