Opera always is installed in C:\Program files.
Most of the preferences, bookmarks, and so on is, for me, under Docs and setting\me\ApplicationData\Opera - check Opera's Help > About, it'll tell where things are.
So, at this point I'm confused as to what you saw and what you now see.
That said, Opera is listed in Avast's Browser integration tab, see pic.
Maybe it has to do what is/was your default browser? Mine is Opera.