As Leo says, you can as they are completely different and independent programs.
I am puzzled as to why Opera 12 would be running when you're not using it though!
You say it's not listed as a running task, but that doesn't mean that it isn't running as a background process.
If you look at the running process list in the Windows Task Manager, is opera.exe listed there?
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If you found the the solution, despite the "Of Topic" you can share it for other users š
And if your original problem has not solved even with a clean profile... the only solution for me it's to test in a Virtual Machine, then a Reset Pc if needed.