Regarding your screenshot, there are actually no create event buttons in that layout. You would have to use the create button in the sidebar or from the dropdown in the header.
I see that you got in
So this is an Admin tools issue
Regarding the event button not showing in the group....
I have now isolated the issue
If you go into the group and then click on the widget item events, this does not show a create event option.
You must click on the event application menu on sidebar or click on the dropdown menu and select create event.
Or you can use the event link in the share status box