Did the DB Cleanup, and it fixed nothing, showing no problems in the Log. Had to delete everything DB related from Local and Roaming M2 folders except accounts.ini, wand.dat and some extra files. Restarted M2, and it re-fetched all messages.
Will see if it works now. What's the right procedure to delete and re-load mail db? I don't want to load Gmail All Mail folders, as they hold all deleted mail too. But they are autoselected at Opera launch after the above folders cleanup. In what files that folders choice is stored?
I had to reinstall M2 completely to keep the right folder choice for each mail acc.