- The kind of tab-switching that v12 had, right-click + mwheel and in last-used order,
This is unlikely to return. The functionality can, however, be recreated using extensions.
Not true as they don't work on internal pages (like the downloads page, or even way worse the new tab page). This is not even close to an alternative.
Right–click on a search field and choose Create Search Engine. Is this not what you meant?
That's it, but it's not working properly. I've set up http://startpage.com as a search, but when I try to use it, Opera Next just opens the page itself.
You most likely made an error. Use this how to: https://support.startpage.com/index.php?/Knowledgebase/Article/View/201/9/how-do-i-install-startpage-as-my-default-search-engine-in-chrome