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?
Middle mouse click also does the trick.
If you found the the solution, despite the "Of Topic" you can share it for other users
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.