I'm not 100% sure CCleaner had anything to do with the Opera installation problems, it may just have been a coincidence that the Opera problems started right away. But as you suggest I get a feeling a deleted some sort of file by mistake when I ran the CCleaner (which I've now removed from my PC).
To answer your questions - yes, when I've tried to reinstall Opera, CCleaner has not even been on my PC because I uninstalled it.
The red Opera icon with the blue/yellow shield is on my desktop and also as a shortcut on my Taskbar. Opera put them in those places when I reinstalled it.
I am installing Opera on my personal PC so I have all the privileges and I am installing Opera into the default folder it suggests when I install.
Just as an aside - when I installed malwarebytes I was able to install and run it but the malwarebytes icon also has the blue/yellow shield and every time I double click it, it says "do you want to allow the following program to make changes to this computer?" message. The only difference between that and Opera is that when I double click the Opera icon and say yes to the message it doesn't load but just keeps hanging there and the browser never opens.