In Firefox, you can ctrl + left-click or shift + left-click to select tabs in the tab bar. Then, you can right-click a selected tab and choose "bookmark tabs" to bookmark all those tabs into a folder. Then, in the bookmarks library in Firefox, you can export your bookmarks to an HTML file. Then, at the URL opera://bookmarks in Opera, you can click the drop-down at the bottom left to import the Firefox bookmarks HTML file. Then, on the opera://bookmarks page, you can right-click that folder of opened tabs you created in Firefox and choose "open all in tabs". Then, you can delete the folder of imported bookmarks to get rid of them.
You can test how this works in a test standalone installation first if you want.
As for session cookies, if importing directly from Firefox doesn't do the trick, use Chrome to import from Firefox and then import from Chrome in Opera to see if that helps. (Didn't test.)