As I expected the problem was in synchronization again. I synchronized only bookmarks and passwords. As a result I have flash and passwords problem. So I had to reset Opera again, then restart system. After that everything works as it must do.
@jimunderscorep .......thanks for the tip, installed 'adobe-flashplugin' as suggested and in a quick test it works as you say, that is, after reactivating flash in Firefox.
In Opera, I need to go into the menu to trigger the 'allow flash' selection periodically......it seems to default to the 'Ask to' selection but I never get asked.