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It seems that in the newest Beta (Opera 60...79) the Dock-Icon issue is fixed, but I've only read the remarks, not tried the Beta version.
Newest version Opera 60.....70. Still the same bugs.
BTW: Do Opera developers sometimes visit this forum?
You' re right. That was a "logical failure" 
but anyway, that doesn't solve the issue.
@xiamenese, well it's strange, but this "Folder"-behavior from the Opera-Icon I have only in the symbolic view (big Icons and the name of the app). Right-clicking this Icon leads to the context-menu of a folder (new folder...information...Import from...etc.). All other Program-Icons are displaying the expected context-menu, as you mentioned (Show Package content...etc.) If I change to List-view, Opera shows also the correct context-menu. For me its strange but reproducible.
I noticed, that the Opera-Icon in the program folder (symbolic view) is not the app itself, if you (right)click on "information", it will indicate, that "Opera" is a folder...
So if you drag this Icon bona fide in your Dock, there is a sort of "folder" instead the app. It seems there is something wrong with the installation itself.
Normally a folder has its Folder-Icon, not the App-Icon.
Thank you for your specification. Your fix isn't working for me. Removed the old Dock-Icon and adding a new has no effect. Still the same issue.
Well, at least I'm not the only one... BTW: Opera Beta still the same issue.